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Nonlinear second order differential equation

  1. Dec 22, 2012 #1
    What is the solution of the follwoing differential equation

    [itex]\frac{\partial^{2}y}{\partial x^{2}}-ay^{-1}\frac{dy}{dx}=0[/itex]

    where [itex]a[/itex] is a constant.
  2. jcsd
  3. Dec 22, 2012 #2


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    Homework Helper

    Use the identity
    [tex]\frac{\mathrm{d}^2y}{\mathrm{d} x^2} = \frac{\mathrm{d}y'}{\mathrm{d}x} =
    \frac{\mathrm{d}y'}{\mathrm{d}y}\frac{\mathrm{d}y}{\mathrm{d}x} = y'\frac{\mathrm{d}y'}{\mathrm{d}y}[/tex]
    to find [itex]y' = \frac{\mathrm{d}y}{\mathrm{d}x}[/itex] as a function of [itex]y[/itex]. Then use separation of variables.
  4. Dec 22, 2012 #3
    Thank you
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