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Substitution differential equation problem

  1. Sep 26, 2011 #1
    Solve y' = y/x + 1/y


    I get a similar answer to the correct one but I believe I am making a substitution error. Here is my attempt:




    dy/dx = y/x + 1/y

    set v = y/x

    equation now becomes: v + x(dv/dx) = v + 1/(x*v)

    reduces to: dv/dx = 1/(x^2 * v)

    Now the equation is seperable, so I seperate and take the integral of both sides yielding:

    v = (sqrt(-2) * sqrt(x*c - 1))/sqrt(x)

    --even if i substitute v = y/x back in it doesn't come out to be the correct solution of:

    y = sqrt(x) * sqrt(x*c -2)



    Any insight would be great!
     
  2. jcsd
  3. Sep 26, 2011 #2
    Nevermind, solved it. Needed to substitute v=y^2.

    Thanks!
     
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