Reduction of order ODE

1. Apr 4, 2010

manenbu

1. The problem statement, all variables and given/known data

Solve:
$$y'' -y' e^{y'^2-y^2} = 0$$

y(0) = 1
y'(0) = 0

2. Relevant equations

3. The attempt at a solution

No idea how to use it.
If I use the substituion y' = p, and y'' = p'p I need to integrate $e^{y^2}$ which is unintegratable. What should I do?

2. Apr 4, 2010

gabbagabbahey

According to your DE and initial conditions, what is $y''(0)$? How about $$\left.\frac{d^n y}{dx^n}\right|_{x=0}$$ ? What might you expect the solution to be if all the derivatives are zero at some point? Can you prove that is the only solution?

3. Apr 4, 2010

manenbu

I get what you're trying to say - that the solution is y=1.
I don't know how to prove it though.