1. Limited time only! Sign up for a free 30min personal 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!

Solving a DE

  1. Sep 18, 2011 #1

    fluidistic

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    I must calculate the general solution to the following (reducible to homogeneous) DE:
    [itex](x^2y^2-1)y'+2xy^3=0[/itex].
    Hint: Use the substitution [itex]y=z^\alpha[/itex].

    2. Relevant equations
    The one given in the hint.


    3. The attempt at a solution
    So I've used the hint. This gave me [itex](x^2z^{2 \alpha }-1)\alpha z^{\alpha -1}+2xz^{3\alpha }=0[/itex].
    I factorized by [itex]z^{\alpha -1}[/itex] and I reach that [itex]z^{\alpha -1}=0[/itex] (thus z=0, thus y=0) or [itex]z^{2\alpha } (\alpha x^2 +2xz)=\alpha[/itex].
    I ran out of ideas on the second condition. ( I don't think back-substituting [itex]z^\alpha =y[/itex] will help).
    Any help is appreciated. Thanks!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Solving a DE
  1. Solve de (Replies: 1)

  2. Solving a DE (Replies: 6)

  3. Solving A DE (Replies: 3)

  4. Solve the DE (Replies: 2)

  5. Solve DE (Replies: 3)

Loading...