# Reduction of order ODE

manenbu

## Homework Statement

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

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

## 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?

## Answers and Replies

Homework Helper
Gold Member
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?

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