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Nonlinear ODE

  1. Nov 18, 2008 #1
    I was looking for some guidance on how to attack this problem.

    Consider the nonlinear ODE:


    (y prime + y squared with A and B constant coefficients)

    Show that the solution is given by y=z'/z, where z(x) solves the second order ODE:


    (z double prime plus z prime with A and B constant coefficients)

    Any advice would be greatly appreciated!

  2. jcsd
  3. Nov 18, 2008 #2


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    Welcome to PF!

    Hi John! Welcome to PF! :smile:

    If y = z'/z, then y' = … ?

    Now subsitute into the original equation, and multiply by z. :smile:
  4. Nov 18, 2008 #3
    Really. Is that all that needs to be done? I did that and got the original equation to look like the second one. So then that makes it a solution for the first equation right? Hmm, I guess that was easy. Thanks!
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