2nd order linear homogeneous differential equations 3 | Khan Academy
A1 A2 B1 B2 C1 C2
initial
US / ɪ'nɪʃl /
•UK / ɪˈnɪʃəl /
- adjecitve
- Existing or occurring at the beginning
- noun
- First letter of your given name
- verb
- To authorize something by writing your initials
simple
US / 'sɪmpl /
•UK / ˈsɪmpəl /
- adjecitve
- Not hard to understand or do; not complex
- Having only a few parts; not complex
- Being ordinary or normal
- Being plain; without a lot added for style
add
US / æd /
•UK / æd /
- verb
- To include as well
- To put two things or numbers together, e.g. 2+2
take
US / teɪk /
•UK / tek /
- 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
original
US / ə'rɪdʒənl /
•UK / əˈrɪdʒənəl /
- adjecitve
- Being first made, thought or performed; fresh
- Being unique or thinking differently from others
they
US / ðeɪ /
•UK / ðe /
- pronoun
- Two or more people, animals, or things
believe
US / bɪ'li:v /
•UK / bɪˈliv /
- verb
- To think or accept that something is true
- To have a particular opinion about something
cancel
US / 'kænsl /
•UK / ˈkænsəl /
- verb
- To end a legal, business, or other agreement
- To stop a planned event from happening
derivative
US / dɪˈrɪvətɪv /
•UK / dɪˈrɪvətɪv /
- adjecitve
- Not from original ideas; from somewhere else
general
US / 'dʒenrəl /
•UK / ˈdʒɛnərəl /
- adjecitve
- Widespread, normal or usual
- noun
- Top ranked officer in the army
multiply
US / ˈmʌltɪplaɪ /
•UK / ˈmʌltəˌplaɪ /
- verb
- To increase in number by reproducing/having babies
- To increase something by a large quantity
- To have increased by a large quantity
- To calculate two numbers e.g. 2 x 4
rewrite
US / ˌri:'raɪt /
•UK / riˈraɪt /
- verb
- To write again to improve, or correct errors
its
US / ɪts /
•UK / ɪts /
- adjecitve
- Referring to or belonging to ‘it’
- determiner
- Of something; belonging or related to something
- other
- Possessive form of “it”
top
US / tɒp /
•UK / tɑp /
- adjecitve
- Being good or great; excellent
- Being the most in degree or quality
- noun
- Item of clothing covering shoulders to waist, hips
- A cover or lid
- Part (e.g. road) that is the furthest away
- Highest or upper part or point of something
- Best or highest status or position
- Flat upper surface or edge of an object
- Child's toy that spins on its point
- Upper section or leaves of fruits and vegetables
- Winning in a sport or contest
- verb
- To be higher or larger than a specific value
- To arrive at the highest point of something
- To put a cover or layer or over something
- To kill; murder
- To hold the highest position on a list
- To be more important, successful or better than
- To beat someone or win at a game
work
US / wɜ:k /
•UK / wɚk /
- 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
figure
US / ˈfiɡə /
•UK / ˈfɪɡjɚ /
- 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
way
US / weɪ /
•UK / we /
- adverb
- Used to emphasize the amount of something
- noun
- Particular aspect of something being thought about
- One of various choices that could be made
- Particular existing condition or state
- (Often long) distance or length of time
- How something is done
- Route to go to a place
- Small street
- Usual behavior, emotions or habits of someone
confusing
US / kənˈfju:zɪŋ /
•UK / kənˈfjuzɪŋ /
- adjecitve
- Being hard to understand
- verb
- To make something unclear or hard to understand
can
US / kæn /
•UK / kən,kæn /
- 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
apply
US / ə'plaɪ /
•UK / əˈplaɪ /
- verb
- To spread a substance or liquid over a surface
- To commit your time and effort to doing something
- To make something useful in a certain situation
- To be relevant for a situation
- To ask formally for (job, permission etc.)
but
US / bət /
•UK / bʌt,bət /
- conjunction
- Used before you say something different, opposite
good
US / ɡʊd /
•UK / ɡʊd /
- adjecitve
- Proper, appropriate or right
- (Of an amount) enough; plenty
- Excellent; high quality
- Acting well or properly; of moral character
- In a positive or happy emotional state
- noun
- Advantage or benefit
give
US / ɡɪv /
•UK / ɡɪv /
- noun
- Degree of flexibility in something, a material
- verb
- To hand over or present something to someone
- To cause someone to have or experience something
color
US / 'kʌlə(r) /
•UK / ˈkʌlɚ /
- 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
our
US / 'aʊə(r) /
•UK / aʊr /
- determiner
- Belonging to us
not
US / nɒt /
•UK / nɑt /
- adverb
- Word indicating the negative
- (Used to form the negative of verbs)
whole
US / həul /
•UK / hol /
- adjecitve
- Complete or full; all of
- Being in a good condition
- noun
- Complete amount or sum; total
equal
US / 'i:kwəl /
•UK / ˈikwəl /
- adjecitve
- Same in shape, size, or number
- verb
- To add up or be the same as
now
US / naʊ /
•UK / naʊ /
- 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
substitute
US / 'sʌbstɪtju:t /
•UK / ˈsʌbstɪˌtut, -ˌtjut /
- noun
- A person or thing acting in place of another
- verb
- To perform the tasks instead of someone else
- To replace one person or thing for another
want
US / wɔnt /
•UK / wɑnt, wɔnt /
- noun
- Something you desire or wish for
- State or condition of poverty
- verb
- To desire or wish for something; hope for a thing
video
US / 'vɪdɪəʊ /
•UK / ˈvɪdiˌo /
- adjecitve
- Of a moving film, with sound
- noun
- Recording capturing action with sound
- verb
- To make a moving film of, with sound
two
US / tu: /
•UK / tu /
- number
- 2
form
US / fɔ:m /
•UK / fɔrm /
- noun
- Sports team or person's current winning record
- Document you complete when making an application
- Visible shape or style; type; kind
- verb
- To organize something such as a club or group
- To develop; to come into a shape or substance
- To make something into a particular shape
out
US / aʊt /
•UK / aʊt /
- 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
minus
US / ˈmaɪnəs /
•UK / ˈmaɪnəs /
- 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
linear
US / ˈlɪniə(r) /
•UK / ˈlɪniər /
- adjecitve
- Made of lines
- Series of progressing from one stage to another
come
US / kʌm /
•UK / kʌm /
- verb
- To arrive at a place
- (Of mail) to be delivered
- To move toward someone; go with someone
- To reach a certain point or state
characteristic
US / ˌkærəktəˈrɪstɪk /
•UK / ˌkærəktəˈrɪstɪk /
- adjecitve
- Typical or distinctive
particular
US / pəˈtɪkjələ(r) /
•UK / pɚˈtɪkjəlɚ, pəˈtɪk- /
- adjecitve
- One specific (one)
- Having firm ideas about what is desirable
- Being special or more than is typical
think
US / θɪŋk /
•UK / θɪŋk /
- verb
- To have an idea about something without certainty
- To have an idea, opinion or belief about something
another
US / əˈnʌðə(r) /
•UK / əˈnʌðɚ /
- adjecitve
- One more, but not this
- determiner
- One more added
- pronoun
- One more (thing)
ton
US / tʌn /
•UK / tʌn /
- noun
- Unit of weight; 907 kilograms (US); 1016 (UK)
and
US / ənd /
•UK / ənd, ən,ænd /
- conjunction
- Used to refer to two or more things
- Plus; in addition; on top of that
- Used to introduce an action that follows another
back
US / bæk /
•UK / bæk /
- adjecitve
- Farthest from the front e.g. in a classroom
- adverb
- Have returned to a place you were before
- noun
- The part of a chair that the upper body leans upon
- Location at the rear of something
- The reverse of side something
- Area on the rear of your body
- verb
- To bet money on something
- To go backwards in a car
- To support and encourage someone or some cause
just
US / dʒʌst /
•UK / dʒʌst /
- 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)
myself
US / maɪˈself /
•UK / maɪˈsɛlf /
- pronoun
- The same person who did the action mentioned
- My regular, usual, or healthy self
those
US / ðəʊz /
•UK / ðoz /
- determiner
- The people or things we are talking about
- pronoun
- The objects far from the speaker
differential
US / ˌdɪfəˈrenʃl /
•UK / ˌdɪfəˈrɛnʃəl /
- adjecitve
- Different, as in treatment; discriminatory
- noun
- A gear to let back wheels spin at different speeds
for
US / fə(r) /
•UK / fɔr,fə /
- preposition
- Used to show the purpose, or need of something
time
US / taɪm /
•UK / taɪm /
- 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
forgot
US / fə'ɡɒt /
•UK / fɚˈɡɑt, fɔr- /
slope
US / sləʊp /
•UK / sloʊp /
- noun
- Angle of a decline, e.g. where a road dips down
- Surface on which people can ski
- verb
- To have one end that is not as high as the other
soon
US / su:n /
•UK / sun /
- adverb
- At a time not long from now
sorry
US / ˈsɒri /
•UK / ˈsɑ:ri /
- exclamation
- What you say to admit you were wrong
- adjecitve
- Causing others to feel pity; poor
- Feeling regret or sympathy about wrong thing
test
US / test /
•UK / test /
- noun
- A medical examination
- Action to establish the truth or nature of
- Examination; questions to measure knowledge
- verb
- To be given a medical examination
- To try to establish the truth or nature of
- To ask a series of questions to measure knowledge
well
US / wel /
•UK / wɛl /
- 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
equation
US / ɪˈkweɪʒn /
•UK / ɪˈkweʒən, -ʃən /
- noun
- Mathematical statement showing things to be equal
- Complex set of different facts, ideas or issues
homogeneous
US / ˌhɒmə'dʒi:nɪəs /
•UK / ˌhoməˈdʒiniəs, -ˈdʒinjəs /
- adjecitve
- Being all of the same type
probably
US / ˈprɒbəbli /
•UK / ˈprɑbəbli /
- adverb
- That is likely to happen or be true
once
US / wʌns /
•UK / wʌns /
- adverb
- One time; one instance
- At a time in the past
- conjunction
- When; as soon as
actually
US / ˈæktʃuəli /
•UK / ˈæktʃuəli /
- adverb
- Used to add new (often different) information
use
US / ju:s /
•UK / ju:s /
- 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
write
US / raɪt /
•UK / raɪt /
- 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
plus
US / plʌs /
•UK / plʌs /
- noun
- A benefit or advantage
- preposition
- In addition; add
- In addition to; Indicates a number above
- Having a value greater than zero
side
US / saɪd /
•UK / saɪd /
- 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
here
US / hɪə(r) /
•UK / hɪr /
- adverb
- In this place; at this location, position or time
try
US / traɪ /
•UK / traɪ /
- noun
- Act of putting the ball over the rugby goal line
- verb
- To make an effort, to attempt to do something
- To examine someone or something in a court of law
- To test to see if it is good or you like it
- To make a person go through hardship; test
- To examine something to see if it works
point
US / pɔɪnt /
•UK / pɔɪnt /
- 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
already
US / ɔ:lˈredi /
•UK / ɔlˈrɛdi /
- adverb
- Having happened or been done before this time
will
US / wɪl /
•UK / wɪl /
- 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
into
US / 'ɪntə /
•UK / ˈɪntu /
- preposition
- Moving or going inside something
- In the same direction as; in the direction of
- So as to become; taking the state of
one
US / wʌn /
•UK / wʌn /
- 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
order
US / 'ɔ:də(r) /
•UK / ˈɔrdɚ /
- 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
solution
US / səˈlu:ʃn /
•UK / səˈluʃən /
- noun
- Mix of a liquid and a solid or a gas
- Way to solve or deal with a problem
let
US / let /
•UK / lɛt /
- verb
- To allow someone to do something
- Introducing a suggestion to do something together
- To rent a house, etc. to others
might
US / maɪt /
•UK / maɪt /
- other
- Used to politely request an action
- Used to express that something could happen
- Power, strength, force or influence
the
US / ðə /
•UK / ðə /
- 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
this
US / ðɪs /
•UK / ðɪs /
- 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
how
US / haʊ /
•UK / haʊ /
- 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)
year
US / jə: /
•UK / jɪr /
- noun
- Unit of time equal to 12 months or 365 or 366 days
- Used to refer to the age of a person
you
US / jʊ /
•UK / ju /
- pronoun
- Person someone is speaking or writing to
- Person or people in general
could
US / kəd /
•UK / kʊd /
- other
- Past form of 'can' to mean have ability
- Used to ask for something politely, or to offer
know
US / nəʊ /
•UK / noʊ /
- 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
end
US / end /
•UK / ɛnd /
- noun
- The point where a process or activity stops
- A point that marks the limit of something; finish
- Goal or desired result
- The tip, edge or limit of something
- verb
- To be the last part of something
prime
US / praɪm /
•UK / praɪm /
- 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
next
US / nekst /
•UK / nɛkst /
- 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
exercise
US / 'eksəsaɪz /
•UK / ˈɛksɚˌsaɪz /
- noun
- Physical activity to increase health and strength
- Set of questions in a text book
- verb
- To work out to become stronger and healthier
- To retain your ability or practice your skills
have
US / həv /
•UK / hæv /
- 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
US / lɑ:st /
•UK / læst /
- 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
with
US / wɪð /
•UK / wɪð, wɪθ /
- 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
see
US / si: /
•UK / si /
- 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)
essentially
US / ɪˈsenʃəli /
•UK / ɪˈsenʃəli /
- adverb
- Basically; (said when stating the basic facts)
right
US / raɪt /
•UK / raɪt /
- 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
example
US / ɪgˈzɑ:mpl /
•UK / ɪɡˈzæmpəl /
- noun
- Thing, person which represents a category
again
US / ə'ɡen /
•UK / əˈɡɛn /
- adverb
- One more time, once more
different
US / ˈdɪfrənt /
•UK / ˈdɪfrənt /
- adjecitve
- Not of the same kind; unlike other things
that
US / ðæt /
•UK / ðæt, ðət /
- 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’
second
US / 'sekənd /
•UK / ˈsɛkənd /
- 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
what
US / wɒt /
•UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /
- pronoun
- Thing or things that; the same kind as
- Used to emphasize something you are about to say
- adjecitve
- Used to refer to a particular amount, or number
- Used to place emphasis on a particular quality
- adverb
- To a certain degree
- determiner
- Question words used for asking for information
- exclamation
- Used to express excitement, shock, or surprise
- Used to ask people to repeat something they said
find
US / faɪnd /
•UK / faɪnd /
- 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
watch
US / wɒtʃ /
•UK / wɑtʃ /
- noun
- Period of time someone is responsible for guarding
- Device you wear on your wrist that shows the time
- Official warning statement, e.g. of bad weather
- verb
- To keep in check, manage, or control something
- To look at something for entertainment, e.g. TV
- To guard a place or people; protect child, etc.
- To look at carefully to work out what is happening
- To protect and care for someone or something
get
US / ɡet /
•UK / ɡɛt /
- 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
first
US / fɜ:st /
•UK / fɚst /
- adjecitve
- 1st; Coming before all others in time or place
- noun
- Something that has not happened before
- Position of the winner of a competition
algebra
US / ˈældʒɪbrə /
•UK / ˈældʒəbrə /
- noun
- Math using letters or symbols in place of numbers
then
US / ðen /
•UK / ðɛn /
- 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
tell
US / tel /
•UK / tɛl /
- 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
solve
US / sɒlv /
•UK / sɑ:lv /
- verb
- To figure out a way to handle a difficult problem