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!