I am having trouble with this problem. I believe that there is a singular solution involved in it yet I do not know how to find it.

(z'')(z^2)=(z')^3

so far i have rewritten the problem as

(z'')(z^2)-(z')^3=0 , made the substitution u=z' and continued to solve that using separation of variables. I still do not understand how to find the singular solution though

thank you for any help