1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

ODE change of variable

  1. Sep 6, 2012 #1
    1. The problem statement, all variables and given/known data

    I have the ODE [itex] y' = f(\frac{y}{x}) [/itex], and I want to re-write this as a separable equation using the change of variable [itex] u = \frac{y}{x} [/itex]

    3. The attempt at a solution

    I use the chain rule to write [itex] y' = \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}
    = \frac{dy}{du}(-\frac{y}{x^2}) = -\frac{dy}{du}\frac{u^2}{y} = f(u) [/itex]

    which is a separable equation. However this seems to be wrong somehow because when I try using it to solve equations of the above form, I'm getting the wrong answer. Any help where I went wrong?
     
  2. jcsd
  3. Sep 6, 2012 #2
    If [itex]u=y/x[/itex] then [itex]y'=x\frac{du}{dx}+u[/itex]
     
  4. Sep 6, 2012 #3
    I don't see how I can use that to put the original equation [itex] \frac{dy}{dx} = f(\frac{y}{x}) [/itex] into separable form though. :\
     
  5. Sep 6, 2012 #4
    Won't you then have the equation:

    [tex]xu'+u=f(u)[/tex]

    Ain't that separable?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook