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!

Quote:

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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!

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