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

Autonomous Second Order ODE

  1. Jul 14, 2009 #1
    Hi All,

    I was looking for the general solution of an equation as y(x)'' = f (y), and found the attached document on the web.

    It presents the solution in a way which I am not sure I understand. I tried to look at the trivila example y'' = - y, solution y = sin (x), but I am struggling in obtaining this result with the provided solution.

    If anybody could help, I would be the most obliged.

    All the Best

    Muzialis
     

    Attached Files:

  2. jcsd
  3. Aug 8, 2009 #2
    Hi,

    The trick is to define a new variable, y'=dy/dx=p(y(x)).
    Now y''=dp/dy*y'=dp/dy*p=f(y).
    Integrating now yields p^2=c+int(f(y))dy. The next step is to integrate dx=dy/p(y).

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




Similar Discussions: Autonomous Second Order ODE
Loading...