Thread: number of solutions for an ode

Here is the question:

How many solutions does y(y')^2 =z have? y(0)=0

Am I right to look at f(z,y) and the partial derivative of f(z,y) wrt to z to see if they are continous in a closed rectangle containing 0?

It looks to me like the partial derivative is not continous in that area, but how does this relate to the number of solutions?

Thanks!

Originally Posted by sarah232

Here is the question:

How many solutions does y(y')^2 =z have? y(0)=0

Am I right to look at f(z,y) and the partial derivative of f(z,y) wrt to z to see if they are continous in a closed rectangle containing 0?

It looks to me like the partial derivative is not continous in that area, but how does this relate to the number of solutions?

Thanks!

Cauchy-Lipschitz theorem says that there is a unique solution if f(z,y) is a Lipschitz function wrt to y.