Nonlinear ODE

1. Apr 4, 2007

Logik

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. Apr 4, 2007

StatMechGuy

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.

3. Apr 4, 2007

Logik

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

thanks

Last edited: Apr 4, 2007