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Homework Help: First Order Differential Equations

  1. Jan 19, 2008 #1
    1. The problem statement, all variables and given/known data

    Solve the following differential equation:

    y' = (y/x) + (2x^3Cos(x^2)/y).

    2. Relevant equations



    3. The attempt at a solution

    You certainly can't separate variables here and you can't put it in the form in which you can find the integrating factor. This is not a Bernoulli equation and neither can it be solved by the y/x = z substitution. I am completely stumped!! Please help.
     
  2. jcsd
  3. Jan 19, 2008 #2
    This is a non-linear ODE. To make it linear multiply by [tex]y(x)[/tex] and observe that

    [tex]y'(x)\,y(x)=\frac{1}{2}\,(y(x)^2)'[/tex]

    and try then the substitution [tex]y(x)^2=z(x)[/tex]
     
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