|Apr4-07, 03:05 PM||#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.
|Apr4-07, 03:10 PM||#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.
|Apr4-07, 03:19 PM||#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
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