Subtitles section
Repeat sentence
Subtitles mode
Full screen
Previous
Next
x 1.0
Playback speed
More

Undetermined coefficients 4 | Second order differential equations | Khan Academy

Video vocabulary

put

Copy vocabulary

US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

two

Copy vocabulary

US / tu: /

UK / tu /

A1
  • number
  • 2

and

Copy vocabulary

US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

call

Copy vocabulary

US / kɔ:l /

UK / kɔl /

A1
  • noun
  • A order or request for action
  • The sound an animal makes, often when in danger
  • A correct prediction, e.g. a decision in a game
  • A short visit to a place or person
  • A decision by a referee or umpire in a game
  • verb
  • To make a request or order for action
  • (Animal) to make sounds to warn of danger
  • To announce the date of an election
  • To make a judgment about something
  • To give someone or something a name
  • To guess in advance the result or outcome
  • To visit a place or person for a short time
  • To phone someone
  • To speak, announce or shout in a loud voice

where

Copy vocabulary

US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

another

Copy vocabulary

US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

most

Copy vocabulary

US / məʊst /

UK / most /

A1
  • adverb
  • Very; extremely
  • Greatest possible degree
  • pronoun
  • Nearly all of something

minus

Copy vocabulary

US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

out

Copy vocabulary

US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

couple

Copy vocabulary

US / 'kʌpl /

UK / ˈkʌpəl /

A2
  • noun
  • Two people in a romantic relationship
  • Two of something; two people; a pair
  • verb
  • To join something to something else
  • (Two animals) to engage in sexual relations
  • To put two people or things together

finally

Copy vocabulary

US / ˈfaɪnəli /

UK / ˈfaɪnəli /

A1
  • adverb
  • used especially at the beginning of a sentence to introduce the last point or idea
  • After a long time or some difficulty

linear

Copy vocabulary

US / ˈlɪniə(r) /

UK / ˈlɪniər /

B1
  • adjecitve
  • Made of lines
  • Series of progressing from one stage to another

something

Copy vocabulary

US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

unwieldy

Copy vocabulary

US / ʌnˈwi:ldi /

UK / ʌnˈwildi /

C1
  • adjecitve
  • Hard to move/control due to its size/shape/weight

prime

Copy vocabulary

US / praɪm /

UK / praɪm /

A2
  • adjecitve
  • Concerning the highest in quality or value
  • Concerning the highest level of achievement
  • Most important, chief importance in value
  • verb
  • To get a person ready for; prepare someone
  • To coat with paint to prepare it for the main coat

with

Copy vocabulary

US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

undetermined

Copy vocabulary

US / 'ʌndɪ'tɜ:mɪnd /

UK / ˌʌndɪ'tɜ:mɪnd /

B1
  • adjecitve
  • Not yet having been ascertained or decided on

see

Copy vocabulary

US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

before

Copy vocabulary

US / bɪˈfɔ:(r) /

UK / bɪˈfɔr,-ˈfor /

A1
  • adverb
  • At a time earlier than the present; previously
  • conjunction
  • In advance of something happening
  • preposition
  • In front of someone or something

have

Copy vocabulary

US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

last

Copy vocabulary

US / lɑ:st /

UK / læst /

A1
  • adjecitve
  • Most recent; the latest
  • The one before
  • adverb
  • Final; with nothing following; after all others
  • Most recent; the latest
  • determiner
  • The one at the end
  • verb
  • To remain or continue for a certain period of time

delete

Copy vocabulary

US / dɪ'li:t /

UK / diˈlit /

B1
  • verb
  • To remove or erase something

could

Copy vocabulary

US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

know

Copy vocabulary

US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

sine

Copy vocabulary

US / saɪn /

UK / saɪn /

C1
  • noun
  • Angle's ratio of side opposite hypotenuse

next

Copy vocabulary

US / nekst /

UK / nɛkst /

A1
  • adverb
  • The one that follows another in time or order
  • At a time or place directly after the present one
  • noun
  • The one that follows after
  • adjecitve
  • Immediately after the previous one
  • First occurrence after the present one

problem

Copy vocabulary

US / ˈprɒbləm /

UK / ˈprɑbləm /

A1
  • adjecitve
  • Causing trouble
  • noun
  • Something difficult to deal with or causes trouble
  • Question to show understanding of a math concept

clean

Copy vocabulary

US / kli:n /

UK / klin /

A1
  • adjecitve
  • Not marked in any way; blank
  • Done according to the rules or standards; fair
  • Free from disease or sickness
  • Being free from dirt or marks; washed
  • Behaving well; not breaking any rules; legal
  • adverb
  • Completely; entirely
  • verb
  • To make free from dirt or marks; washed
  • To make neat and orderly e.g. a room
  • To remove the inner parts of an animal

think

Copy vocabulary

US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

particular

Copy vocabulary

US / pəˈtɪkjələ(r) /

UK / pɚˈtɪkjəlɚ, pəˈtɪk- /

B2
  • adjecitve
  • One specific (one)
  • Having firm ideas about what is desirable
  • Being special or more than is typical

type

Copy vocabulary

US / taɪp /

UK / taɪp /

A1
  • noun
  • Printed letters or blocks used for printing them
  • Group of things or people sharing common features
  • verb
  • To identify something belonging to a group
  • To write by touching keys on a keyboard

find

Copy vocabulary

US / faɪnd /

UK / faɪnd /

A1
  • noun
  • Object discovered by chance
  • Things that have been discovered from searching
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

case

Copy vocabulary

US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

second

Copy vocabulary

US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon

that

Copy vocabulary

US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

like

Copy vocabulary

US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

right

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

baby

Copy vocabulary

US / ˈbeɪbi /

UK / ˈbeɪbi /

A2
  • adjecitve
  • Small in size; smaller than usual
  • noun
  • A very young child, who cannot yet speak
  • verb
  • To treat someone as if they were newly born

then

Copy vocabulary

US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

solve

Copy vocabulary

US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

tell

Copy vocabulary

US / tel /

UK / tɛl /

A1
  • verb
  • To (strongly) advise a person to do something
  • To be able to guess
  • To say or communicate information to someone
  • To inform, but without speaking; indicate
  • To have a negative effect on someone
  • To order someone to do something; command
  • To recognize something based on certain signs
  • To report something to an authority
  • To explain something or teach someone something

square

Copy vocabulary

US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

interesting

Copy vocabulary

US / ˈɪntrəstɪŋ /

UK / ˈɪntrɪstɪŋ, -tərɪstɪŋ, -təˌrɛstɪŋ /

A1
  • adjecitve
  • Taking your attention; making you want to know
  • verb
  • To make someone want to know about something
  • To persuade to do, become involved with something

bunch

Copy vocabulary

US / bʌntʃ /

UK / bʌntʃ /

B1
  • noun
  • A group of things of the same kind
  • verb
  • To group people or things closely together
  • (Cloth) to gather/be gathered together in folds

each

Copy vocabulary

US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

method

Copy vocabulary

US / 'meθəd /

UK / ˈmɛθəd /

A2
  • noun
  • (Organized and planned) way of doing something

first

Copy vocabulary

US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

Copy vocabulary

US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

write

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

use

Copy vocabulary

US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

actually

Copy vocabulary

US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

continue

Copy vocabulary

US / kən'tɪnju: /

UK / kənˈtɪnju /

A1
  • verb
  • To do something without stopping, or after pausing
  • To start doing again after a break, pause, or stop

complicated

Copy vocabulary

US / 'kɒmplɪkeɪtɪd /

UK / ˈkɑmplɪˌketɪd /

B1
  • adjecitve
  • Difficult to do, understand or use
  • verb
  • To make more difficult to do, understand or use

will

Copy vocabulary

US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

many

Copy vocabulary

US / 'menɪ /

UK / ˈmɛni /

A1
  • determiner
  • Used to refer a large number of things

daunt

Copy vocabulary

US / dɔ:nt /

UK / dɔnt, dɑnt /

B2
  • verb
  • To make someone feel less courageous or confident

already

Copy vocabulary

US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

switch

Copy vocabulary

US / swɪtʃ /

UK / swɪtʃ /

A2
  • noun
  • A change or shift from one method to another
  • Thing you move to turn electrical items on or off
  • Thin flexible piece of wood or stick
  • verb
  • To exchange or replace something for another thing

sure

Copy vocabulary

US / ʃʊə(r) /

UK / ʃʊr /

A1
  • adjecitve
  • Having no doubts about something
  • Have confidence in your own words or actions
  • Firmly established or held; being firm or stable
  • Being correct or true
  • adverb
  • What you say to agree willingly

point

Copy vocabulary

US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

probably

Copy vocabulary

US / ˈprɒbəbli /

UK / ˈprɑbəbli /

A1
  • adverb
  • That is likely to happen or be true

homogeneous

Copy vocabulary

US / ˌhɒmə'dʒi:nɪəs /

UK / ˌhoməˈdʒiniəs, -ˈdʒinjəs /

B1
  • adjecitve
  • Being all of the same type

four

Copy vocabulary

US / fɔ:(r) /

UK / fɔr, for /

A1
  • number
  • 4

side

Copy vocabulary

US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

plus

Copy vocabulary

US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

past

Copy vocabulary

US / pɑ:st /

UK / pæst /

A2
  • adjecitve
  • No longer current or new
  • adverb
  • So as to go beyond, or further than something
  • noun
  • Time that existed before now, e.g. long ago
  • preposition
  • After a particular time
  • At a later point in distance; beyond

fairly

Copy vocabulary

US / 'feəlɪ /

UK / ˈfɛrli /

A2
  • adverb
  • Quite; pretty; between very and a little
  • In a manner that is right and acceptable

never

Copy vocabulary

US / 'nevə(r) /

UK / ˈnɛvɚ /

A1
  • adverb
  • Not ever; not at any time

time

Copy vocabulary

US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

for

Copy vocabulary

US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

differential

Copy vocabulary

US / ˌdɪfəˈrenʃl /

UK / ˌdɪfəˈrɛnʃəl /

B2
  • adjecitve
  • Different, as in treatment; discriminatory
  • noun
  • A gear to let back wheels spin at different speeds

just

Copy vocabulary

US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

line

Copy vocabulary

US / laɪn /

UK / laɪn /

A1
  • noun
  • Border that divides two places or regions
  • Long crease in the skin, often from age
  • Mark that is long, straight and very thin
  • Row of words, letters or numbers that are written
  • Telephone connection
  • People waiting one behind the other; queue
  • Long thin wire, e.g. for electrical signal
  • verb
  • To put material along the inside of something

well

Copy vocabulary

US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

start

Copy vocabulary

US / stɑ:t /

UK / stɑrt /

A1
  • noun
  • First time or place that a thing exists; beginning
  • First opportunity to achieve something, e.g. a job
  • Sudden action or movement because you are scared
  • other
  • Beginning of something in place or time
  • verb
  • To do, be or happen for the first time; begin
  • To turn something on

depend

Copy vocabulary

US / dɪˈpend /

UK / dɪˈpend /

B1
  • verb
  • Be controlled or determined by (someone/something)

equation

Copy vocabulary

US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

board

Copy vocabulary

US / bɔ:d /

UK / bɔrd, bord /

A1
  • noun
  • Surface for posting or showing information
  • Group of persons who direct an organization
  • Long piece of material used for riding the waves
  • Long thin piece of wood, used for building; plank
  • verb
  • To enter a ship, plane, or other vehicle
  • To cover with long wooden strips of wood
  • To pay money to live in someone's house; lodge

constant

Copy vocabulary

US / 'kɒnstənt /

UK / ˈkɑnstənt /

A2
  • adjecitve
  • Happening frequently or without pause
  • noun
  • Thing that happens always or at a regular rate

tremendously

Copy vocabulary

US / trə'mendəslɪ /

UK / trɪˈmɛndəslɪ /

B1
  • adverb
  • Very well or very impressively

sorry

Copy vocabulary

US / ˈsɒri /

UK / ˈsɑ:ri /

A1
  • exclamation
  • What you say to admit you were wrong
  • adjecitve
  • Causing others to feel pity; poor
  • Feeling regret or sympathy about wrong thing

three

Copy vocabulary

US / θri: /

UK / θri /

A1
  • number
  • Number 3

term

Copy vocabulary

US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

able

Copy vocabulary

US / 'eɪbl /

UK / ˈebəl /

A2
  • adjecitve
  • Skilled; good at something
  • Having the ability to do something

solution

Copy vocabulary

US / səˈlu:ʃn /

UK / səˈluʃən /

A2
  • noun
  • Mix of a liquid and a solid or a gas
  • Way to solve or deal with a problem

follow

Copy vocabulary

US / ˈfɔləu /

UK / ˈfɑlo /

A1
  • verb
  • To come after someone; be guided by someone
  • To support someone, e.g. singer or comedian
  • To be the logical result of something
  • To happen after something else happens
  • To believe a set of values or a moral teacher
  • To understand something happening or being said

coefficient

Copy vocabulary

US / ˌkəʊɪˈfɪʃnt /

UK / ˌkoʊɪˈfɪʃnt /

B2
  • adjecitve
  • Number by which another number is multiplied

one

Copy vocabulary

US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

this

Copy vocabulary

US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

expose

Copy vocabulary

US / ɪk'spəʊz /

UK / ɪkˈspoʊz /

A2
  • noun
  • News article revealing secret information
  • verb
  • To make visible, without covering or protection
  • To allow light through a cameras lens onto film
  • To be talked about in the media
  • To make a secret known to the public
  • To experience something, often a harmful thing

you

Copy vocabulary

US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

how

Copy vocabulary

US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

order

Copy vocabulary

US / 'ɔ:də(r) /

UK / ˈɔrdɚ /

A1
  • noun
  • Religious or social group, as of nuns
  • Instructions to others to do what you want
  • State in which things are neat and organized
  • What you ask to buy, e.g. food in restaurant
  • Social or political control of an area
  • verb
  • To put things in a sequence, e.g. a, b, c
  • To give instructions to others to do what you want
  • To ask for something you want to buy, e.g. a meal

make

Copy vocabulary

US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

wow

Copy vocabulary

US / waʊ /

UK / waʊ /

A1
  • exclamation
  • Sound people make when they make are impressed
  • verb
  • (Informal) to greatly impress someone

the

Copy vocabulary

US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

might

Copy vocabulary

US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

let

Copy vocabulary

US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

alone

Copy vocabulary

US / ə'ləʊn /

UK / əˈlon /

A1
  • adjecitve
  • Apart from others
  • Without equal
  • adverb
  • Without anyone or anything else

realization

Copy vocabulary

US / ˌri:əlaɪˈzeɪʃn /

UK / ˌri:ələˈzeɪʃn /

B1
  • noun
  • Act of noticing something not noticed before

look

Copy vocabulary

US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

general

Copy vocabulary

US / 'dʒenrəl /

UK / ˈdʒɛnərəl /

A1
  • adjecitve
  • Widespread, normal or usual
  • noun
  • Top ranked officer in the army

derivative

Copy vocabulary

US / dɪˈrɪvətɪv /

UK / dɪˈrɪvətɪv /

B1
  • adjecitve
  • Not from original ideas; from somewhere else

they

Copy vocabulary

US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

everything

Copy vocabulary

US / 'evrɪθɪŋ /

UK / ˈɛvriˌθɪŋ /

A1
  • pronoun
  • All of the things mentioned

space

Copy vocabulary

US / speɪs /

UK / spes /

A1
  • noun
  • Empty area kept for a specific reason, like a car
  • Empty area with nothing in it
  • Area in the sky where the stars are
  • Area between written words on a page
  • verb
  • To make a certain distance or time between

initial

Copy vocabulary

US / ɪ'nɪʃl /

UK / ɪˈnɪʃəl /

A2
  • adjecitve
  • Existing or occurring at the beginning
  • noun
  • First letter of your given name
  • verb
  • To authorize something by writing your initials

hairy

Copy vocabulary

US / ˈheəri /

UK / ˈheri /

A2
  • adjecitve
  • Having or covered with a lot of hair

change

Copy vocabulary

US / tʃeɪndʒ /

UK / tʃendʒ /

A1
  • noun
  • Exchange of one set of clothes for another
  • Money in the form of coins instead of paper
  • Money returned after giving too much
  • Act of making or becoming something else
  • verb
  • To exchange one set of clothes for another
  • To exchange one kind of money for another
  • To replace something with another thing
  • To make or become something else
  • To go from one train, bus, etc. and go to another

work

Copy vocabulary

US / wɜ:k /

UK / wɚk /

A1
  • adjecitve
  • Activity completed in order to make money
  • noun
  • The product of some artistic or literary endeavor
  • Everything created by an author, artist, musician
  • Activity you do in order to make money
  • Place of employment
  • Final product or result of a some labor or effort
  • verb
  • To bring into a specific state of success
  • To be functioning properly, e.g. a car
  • To do your job in your company or workplace
  • To make an effort to do something
  • To operate a machine or device

polynomial

Copy vocabulary

US / ˌpɒlɪ'nəʊmɪəl /

UK / ˌpɒlɪ'noʊmɪrl /

A1
  • adjecitve
  • Having the character of a polynomial

useful

Copy vocabulary

US / ˈju:sfl /

UK / ˈjusfəl /

A1
  • adjecitve
  • That can help with a particular task

move

Copy vocabulary

US / mu:v /

UK / muv /

A1
  • noun
  • Act of moving a playing piece in chess, etc.
  • An action; doing something
  • Step taken to achieve a goal
  • verb
  • To cause someone to have certain emotions
  • To cause something to change to a different place
  • To change where people live or a business operates
  • To take action to do or achieve something

figure

Copy vocabulary

US / ˈfiɡə /

UK / ˈfɪɡjɚ /

A1
  • noun
  • Your body shape
  • Numbers in a calculation
  • Doll-like thing meant to represent a person
  • Picture or diagram giving information in a text
  • Person who is very important or famous
  • Shape of a person seen indistinctly or in outline
  • Amount that is expressed in numbers
  • verb
  • To appear in a game, play or event
  • To calculate how much something will cost
  • To understand after thinking; work out

ago

Copy vocabulary

US / əˈgəʊ /

UK / əˈgoʊ /

A1
  • adverb
  • At a specified length of time in the past

take

Copy vocabulary

US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

add

Copy vocabulary

US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

all

Copy vocabulary

US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

would

Copy vocabulary

US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

really

Copy vocabulary

US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

blue

Copy vocabulary

US / blu: /

UK / blu /

A1
  • adjecitve
  • Color of the clear sky
  • Feeling sad or down

same

Copy vocabulary

US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

can

Copy vocabulary

US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

not

Copy vocabulary

US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

color

Copy vocabulary

US / 'kʌlə(r) /

UK / ˈkʌlɚ /

A1
  • noun
  • Quality of things you can see, e.g. red, blue
  • Pink or red in your face, e.g. after being ill
  • The shade of someone's skin e.g. black, or yellow
  • verb
  • To change or affect someone's opinion
  • To make something colorful using colored pencils

video

Copy vocabulary

US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

want

Copy vocabulary

US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

sum

Copy vocabulary

US / sʌm /

UK / sʌm /

A2
  • noun
  • Amount when all is added together; total
  • verb
  • To add two or more numbers together; total

now

Copy vocabulary

US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

equal

Copy vocabulary

US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

but

Copy vocabulary

US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

sense

Copy vocabulary

US / sens /

UK / sɛns /

A1
  • noun
  • Certain mental feeling or emotion
  • Normal or clear state of mind
  • Meaning of a particular word, phrase or text
  • verb
  • To perceive using sight, sound, taste touch etc.
  • To recognize the presence of something
  • Subtitles section
  • Before we move on past the method of undetermined coefficients, I want to make and interesting and actually a useful point.
  • Let's say that I had the following nonhomogeneous differential equation: the second derivative of y minus 3 times the first derivative minus 4y is equal to-- now this is where gets interesting-- 3e to the 2x plus 2 sine of x plus-- let me make sure that I'm doing the same problems that I've already worked on-- plus 4x squared.
  • So you might say, wow, this is a tremendously complicated problem.
  • I have the 3 types of functions I've been exposed to, I would have so many undetermined coefficients, it would get really unwieldy.
  • And this is where you need to make a simplifying realization.
  • We know the three particular solutions to the following differential equations.
  • We know the solution to the second derivative minus 3 times the first derivative minus 4y.
  • Well, this is this the homogeneous, right?
  • And we know that the solution to the homogeneous equation-- we did this a bunch of times-- is C1e to the 4x plus C2e to the minus x.
  • We know the solution to-- and I'll switch colors, just for a variety-- y prime prime minus 3y prime minus 4y is equal to just this alone: 3e to the 2x.
  • And we saw that that particular solution there, y particular, was minus 1/2 e to the 2x.
  • And we did this using undetermined coefficients.
  • We did that a couple of videos ago.
  • And then let me just write this out a couple of times.
  • We know the solution to this one, as well.
  • This was another particular solution we found.
  • I think it was two videos ago.
  • And we found that the particular solution in this case-- and this was a fairly hairy problem-- was minus 5/17 x plus 3/17.
  • Sorry.
  • The particular solution was minus 5/17 sine of x plus 3/17 cosine of x.
  • And then finally this last polynomial, we could call it.
  • We know the solution when that was just the right-hand side.
  • That was this equation.
  • And there we figured out-- and this was in the last video.
  • We figured out that the particular solution in this case was minus x squared plus 3/2 x minus 13/8.
  • So we know the particular solution when 0's on the right-hand side.
  • We know it when just 3e to the 2x is on the right-hand side.
  • We know it just when 2 sine of x is on the right-hand side.
  • And we know it just when 4x squared is on the right-hand side.
  • First of all, the particular solution to this nonhomogeneous equation, we could just take the sum of the three particular solutions.
  • And that makes sense, right?
  • Because one of the particular solutions, like this one when you put it on the left-hand side, it will just equal this term.
  • This particular solution, when you put it in the left-hand side, will equal this term.
  • And finally, this particular solution, when you put it on the left-hand side, will equal the 4x squared.
  • And then you could add the homogeneous solution to that.
  • You put it in this side and you'll get 0.
  • So it won't change the right-hand side.
  • And then you will have the most general solution because you have these two constants that you can solve for depending on your initial condition.
  • So the solution to this seemingly hairy differential equation is really just the sum of these four solutions.
  • Let me clean up some space because I want everything to be on the board at the same time.
  • So the solution is going to be-- well, I want that to be deleted.
  • I'll do it in baby blue.
  • Is going to be the solution to the homogeneous C1e to the 4x plus C2e to the minus x minus 1/2 e the to 2x.
  • And I'll continue this line.
  • Minus 5/17 sine of x plus 3/17 cosine of x minus x squared plus 3/2 x minus 13/8.
  • And it seems daunting.
  • When you saw this, it probably looked daunting.
  • This solution, if I told you this was a solution and you didn't know how to do undetermined coefficients, you're like, oh, I would never be able to figure out something like that.
  • But the important realization is that you just have to find the particular solutions for each of these terms and then sum them up.
  • And then add them to the general solution for the homogeneous equation, if this was a 0 on the right-hand side.
  • And then you get the general solution for this fairly intimidating-looking second order linear nonhomogeneous differential equation with constant coefficients.
  • See you in the next video, where we'll start learning another method for solving nonhomogeneous equations.