A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
can anyone explain me the form of first and higher order linear differential equation? I know the form of linear differential equation. e.g.
y''xy'+2y=0. So what will happen to this equation if the coefficient of y' is y?
anonymous
 one year ago
can anyone explain me the form of first and higher order linear differential equation? I know the form of linear differential equation. e.g. y''xy'+2y=0. So what will happen to this equation if the coefficient of y' is y?

This Question is Open

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.0A simple example where the coefficient of the highest order term (y') : is y \[y\cdot y'=a\] Because the coefficient is not a constant, this equation is nonlinear.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0While you are correct with your example being nonlinear, in general the nonconstancy of coefficients is insufficient to classify an ODE as nonlinear. As the poster noted, their ODE was a linear ODE even though the coefficient on the y' term is a function of x namely f(x)=x. A better way of stating it is that as long as the "coefficient" (aka the function) multiplying each term is not a function of the independent variable (y) or its derivatives, then the ODE is linear. Otherwise the ODE is nonlinear. The example you provided is precisely such a term that would make an ODE nonlinear. Other examples of nonlinear terms y^2 or (y')^2.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.