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Homework Help: 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
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