A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

xy'+y=y2. first order nonlinear differential equation. Why can't i solve this by writing xy'+y as (xy)' and then integrating both sides wrt x?

  • This Question is Open
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    in other words, prove why the method of multiplying by mu for linear equations do not work for nonlinear ones.

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Jesstho.-. @sweetburger

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, the idea behind multiplying by mu in a linear equation is to create that product rule derivative, much in the manner that you suggested to rewrite as (xy)'. But with non-linear, that mu may or may not exist and if it does, it certainly wouldnt be found in the same manner. I can't prove that, but the same method doesnt work because you wouldnt be able to find a guaranteed/plausible method for finding that mu, if it exists. As for your suggestion of rewriting and then integrating both sides with respect to x, that fails because you wouldn't have a proper separation of variables. Keep in mind that in the linear case, you always have a function of x alone on the other side of the equality, but in this case you do not. The ideas behind the normal linear case just simply don't apply here. That may not be quite the answer you're looking for, but thats how I see it.

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[xy \prime+y=y^2\] divide by y^2 \[x y ^{-2}y \prime+y ^{-1}=1\] \[put~ y ^{-1}=t\] \[-y ^{-2}y \prime=t \prime \] \[-xt \prime+t=1\]

  5. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.