1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find all solutions?

  1. Oct 8, 2014 #1
    1. The problem statement, all variables and given/known data
    Find all solutions of xy'=x^3+(1-2x^2)y+xy^2.

    2. Relevant equations
    None

    3. The attempt at a solution
    Here's my work:

    xy'=x^3+y-2x^2*y+xy^2
    xy'=x(x^2-2xy+y^2)+y
    xy'=x(x-y)^2+y
    y'=(x-y)^2+y/x
    Now I'm stucked. Please help me.
     
  2. jcsd
  3. Oct 8, 2014 #2

    pasmith

    User Avatar
    Homework Helper

    You can see from the last line that [itex]y(x) = x[/itex] is one solution, although there may be others. But your rearrangement is not separable, so you are unlikely to make further progress.

    The left hand side of the original is [itex]xy'[/itex]. There's a [itex]y[/itex] on the right, so bringing that across makes the LHS [itex]xy' - y = x^2(y/x)'[/itex], so the substitution [itex]v = y/x[/itex] is worth considering.
     
  4. Oct 9, 2014 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Good idea!

    If v= y/x, then y= xv so that y'= xv'+ v. xy'=x^3+y-2x^2*y+xy^2 becomes x^2v'+ xv= x^3+ xv- 2x^3v+ x^3v^2.
     
  5. Oct 9, 2014 #4
    Thank you so much for the help, Hallsoflvy.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Find all solutions?
  1. Find all solutions? (Replies: 20)

Loading...