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Need help with non-linear ODE IVP

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data
    given: (y-xy)y' = y^(2) + 1 y(0)=0

    2. Relevant equations

    So I subbed y^(2) = u

    3. The attempt at a solution

    w/ u=y^(2) i got...

    (y-xy)y' = y^(2) + 1
    (1-x)yy' = y^(2)
    (1-x)(u'/2) = u + 1

    and it is here that I am stuck! I [think] I have to put it into the form u' + g(x)*y = b(x) but I can't do it! It is driving me crazy, I have been working on this single problem for over an hour, I am about to lose my sanity, especially since it's ALGEBRA that's tripping me up.

    Any help would be greatly appreciated.

    I was thinking of trying u = (y^(2) + 1) but I feel like that's leading me to nowhere as well.

    Thanks in advance
  2. jcsd
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