Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    pasmith

    User Avatar
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook