1. Not finding help here? Sign up for a free 30min 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!

Nonlinear ODE

  1. Apr 4, 2007 #1
    1. The problem statement, all variables and given/known data

    I have to find the solution of (1) and show that it is not unique if y(0) = 0.
    I can prove it is not unique by using Picard's theorem but I don't know how to find the non trivial solution.

    2. Relevant equations

    (1) y(t)' = Sqrt(y(t))

    3. The attempt at a solution

    I don't know where to start... We have not seen how to solve nonlinear ODE's. A link to a technique or explanation to how to solve it would be very helpful. I'm not looking for the answer, I can get it with Mathematica... I want to understand how to get there.
  2. jcsd
  3. Apr 4, 2007 #2
    You can directly integrate that function:

    dy/dt = y^1/2 => y^(-1/2) dy = dt

    Nontrivial solution. However, you'll find the trivial y(t) = 0 is a perfectly good solution to those initial conditions as well.
  4. Apr 4, 2007 #3
    wow I'm so stupid...

    dy/dt = y^(1/2)
    dy/y^(1/2) = dt
    2y^(1/2) = t + c
    y^(1/2) = 2t + 2c
    y = 4t^2 + 8tc + c^2

    Last edited: Apr 4, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Nonlinear ODE
  1. Nonlinear ODE (Replies: 1)

  2. Nonlinear ODE (Replies: 4)

  3. Nonlinear ODE (Replies: 4)