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

First order nonlinear differential equation Help needed.

  1. Sep 7, 2011 #1
    Hi All,

    I have been trying to solve following nonlinear differential equation, but I couldn't solve it.

    0 = a*[f(t)]^{z/(z-1)} + (-t+C)*f(t) + b*[df(t)/dt]

    where a, b and C are constants and 0< z<1.

    Could you please help me how to solve this nonlinear differential equation? I would really appreciate any suggestions. Many thanks, in advance!

  2. jcsd
  3. Sep 7, 2011 #2
  4. Sep 7, 2011 #3
    Thanks a lot for the suggestion, but unfortunately I could not make integrating factor technique work since integrating factors turns out to be a function of both "t" and "f". Any other suggestions?

    Kind regards
  5. Sep 7, 2011 #4
    I got a suggestion: When you get stuck, fall back and work on a simpler one first, then build it back up to the original problem:


    now, what happens if I let [itex]u=f^{1/2}[/itex]

    you can convert that to a DE in u right?. You know, f=u^2, f'=2uu'. You can do that? Ok, put all that back in, solve it for u, then of course f=u^2. Ok, how about:


    same dif. Let u=f^{1/4}. Now when you figure out what u is, then raise it to the fourth power to get f.

    How about:


    How about when n/m is not rational?
    Last edited: Sep 7, 2011
  6. Sep 7, 2011 #5
    I will definitely try to solve it in the way that you suggested jackmell. Thanks a lot!

    As a quick note, z/(z-1) is negative; hence it may cause some problems.
  7. Sep 7, 2011 #6
    As I said, z/(z-1) taking negative values is very problematic, therefore unfortunately, I could not solve the ODE using the approach you suggested, jackmall. I appreciate your time, though.

    Any other suggestions would be highly appreciated.

    Kind regards
  8. Sep 8, 2011 #7


    then what happens if we let:




    then what happens if we let:

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook