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Homogeneous now seperable ODE

  1. Mar 3, 2012 #1
    [Ok so I have transformed a
    1st order homogenous ODE into a seperable ODE. However I am having trouble seperating to get y on it's own.

    Here's the problem:

    du/dx=(2u^2)/x where u = y/x

    du/(2u^2)=dx/x <<can't get tex to work

    -1/(4u^2)=ln(x)+C=ln(Ax) <<can't get tex to work

    1=-4u^2ln(Ax)

    1=-4(y^2/x^2)ln(Ax)

    y^2=-4x^2ln(Ax)

    y=i2xsqrt(lnAx)


    Is this algebra correct? Is this the right solution? I'm not sure about bringing the y^2 over to the left is ok.
     
  2. jcsd
  3. Mar 3, 2012 #2
    I realise now, I messed up the integration.

    The general solution is:

    y=-x/(ln(Ax^2))
     
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