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Homework Help: 2nd order DE

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data

    y''+(y')2 = y, y(0)=1, y'(0)=1/√2

    2. Relevant equations

    Bernoulli's method.

    3. The attempt at a solution

    Using the substitution p=y' I get this:
    p'p + p2 = y, so I can use z=p2 to solve this.
    However, I'm getting something wrong.
    I think it could be because I'm having too much letters - p, z, y, x so I might be missing some chain rules.
  2. jcsd
  3. Dec 6, 2009 #2
    Not worked through this, but using the substitution p = y', surely you would get:

    p'+p^2 = y and NOT p'p +p^2?
  4. Dec 6, 2009 #3
    but I'm using p(y), not p(x)
    so y'' = dp/dy dy/dx = dp/dy p = p' p
  5. Dec 6, 2009 #4
    oh well, I got it. Took me 2 pages of text. If you're interested I can post the solution here. :)
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