What is an ODE y''+p(x)y'+q(x)y=r(x) Yp(x)=k₁cos(ωx)+k₂sin(ωx) α=min{a,b/k} an equation that contains a derivative of an unknown function, y(x)

an equation that contains a derivative of an unknown function, y(x)

How to transform a non-separable ODE to separable y(x)=C₁x^m₁+C₂x^m₂ You must use substitution for the part you cant separate, usually u=y/x x²y''+pxy'+qy=0 *coefficients same order as y* α=min{a,b/k}

You must use substitution for the part you cant separate, usually u=y/x

how to convert a first order non-linear ode to linear y'+p(x)y=0 let u=y¹⁻ⁿ, Create a new ODE using the equation u'+(1-n)p(x)u=(1-n)r(x) m²+(p-1)m+q=0 S(t)=S₀e^(rt)+(k/r)(e^(rt)-1), where S₀ is the initial investment, k is the investment per year, r is the interest rate, and t is time in years

let u=y¹⁻ⁿ, Create a new ODE using the equation u'+(1-n)p(x)u=(1-n)r(x)

how to solve an exact ODE` check exactness, find U(x,y) such that du/dx=M(x,y) or du/dy=N(x,y) remember to add K. Take the derivative of this U(x,y) with respect to whichever variable not used in the step before, compare this to du/dx or du/dy in step 2 to find K' and integrate if f(x,y) is continuous and bounded over a range R, the IVP has at least one solution over the interval |x-x0|<α x²y''+pxy'+qy=0 *coefficients same order as y* y'+p(x)y=0

check exactness, find U(x,y) such that du/dx=M(x,y) or du/dy=N(x,y) remember to add K. Take the derivative of this U(x,y) with respect to whichever variable not used in the step before, compare this to du/dx or du/dy in step 2 to find K' and integrate

ODEs Final

Flashcard

Learn Mode

Match

Library

Create

Flashcards

Library

Match (Coming Soon)

Calculus - Geometry

user_hassanuml Created by 6 mon ago

Cards in this deck(46)

What is an ODE

How to transform a non-separable ODE to separable

first order linear homogeneous form

how to solve a first order linear homogeneous ODE

first order linear non-homogeneous form

how to solve a first order linear non-homogeneous ODE

first order non-linear form

how to convert a first order non-linear ode to linear

How to check if an ODE is exact

how to solve an exact ODE`

If given an ODE of the form y'=f(x,y), y(x0)=y0, how do you know if there exists a solution to this ode

If given an ODE of the form y'=f(x,y), y(x0)=y0, how do you know if there exists one and only one solution to this ode

how to find alpha when solving for uniqueness and existance

what is a, b, and k when solving for alpha in uniqueness and existence problems

what is the fundamental theorem of second order linear ODEs

when can you use reduction of order, how to do steps

Given one solution of a second order linear ODE, what are the steps to find another solution

what is the general form of a second order homogeneous linear ODE with constant coefficients

what is the characteristic equation for a second order homogeneous linear ODE with constant coefficients

what is the solution of a second order, constat coefficient, homogeneous, linear ODE with two real distinct roots

what is the solution of a second order, constat coefficient, homogeneous linear ODE with one real root

what is the solution of a second order, constat coefficient, homogeneous linear ODE with two complex roots

what is the form of a second order euler-cauchy equation

what is the characteristic equation for a second-order, homogeneous, linear ODE with non-constant coefficients (euler-cauchy)

what is the solution for a second order, homogeneous, linear ODE with non-constant coefficients (euler-cauchy) where the characteristic equation results in two real distinct roots

what is the solution for a second order, homogeneous, linear ODE with non-constant coefficients (euler-cauchy) where the characteristic equation results in one real roots

what is the solution for a second order, homogeneous, linear ODE with non-constant coefficients (euler-cauchy) where the characteristic equation results in two complex roots

form of a second order, non-homogeneous, linear ODE with constant coefficients

what are the steps to solving a non-homogeneous second order ODE

what is the equation for Yp(x) if r(x)=kcos(ωx)

what is the equation for Yp(x) if r(x)=ksin(ωx)

what is the equation for Yp(x) if r(x)=ke^(λx)

what is the equation for Yp(x) if r(x)=kxⁿ

what is the modify rule for non-homogeneous ODEs

what is the sum rule for non-homogeneous ODEs

what is the form of an nth order, linear, non-homogeneous ODE

what is the concept behind Wronskians theorem

what is the characteristic equation of a higher order, homogeneous, linear ODE

what is the solution of a higher order, constant coefficient, homogeneous, linear ODE with real distinct roots

what is the solution of a higher order, constant coefficient, homogeneous, linear ODE with non-repeating, complex roots

what is the solution of a higher order, constant coefficient, homogeneous, linear ODE with real roots repeating n times

what is the solution of a higher order, constant coefficient, homogeneous, linear ODE with complex roots repeating n times

higher order euler cauchy form

how to solve a higher order euler cauchy equation

how to solve a higher order, non-homogeneous ODE

equation to solve modeling problems

Ask Our AI Tutor

Get Instant Help with Your Questions

Need help understanding a concept or solving a problem? Type your question below, and our AI tutor will provide a personalized answer in real-time!

How it works

Ask any academic question, and our AI tutor will respond instantly with explanations, solutions, or examples.

Get Started

Browse questions and discover topic-based flashcards
Practice with engaging flashcards designed for each subject
Strengthen memory with concise, effective learning tools

Discover By Topic

ODEs Final

Related Decks