How Can solve a n order Differential Equations

Question

How can I solve the following equation? what is the h(z)

(z^n+1).|h'(z)|^n=const

Is it possible to use MATLAB?

Answer 1

This is not an n-th order ODE but a first order implicit ODE. Depending on if it is complex, it might even be incomplete or unsolvable, since the absolute value over the derivative introduces an unknowable phase in the isolation of the same.

Without the absolute value, i.e. as

(1+z^n)*h'(z)^n = C

you will have to care to correct for a continuous phase in reps. after the n-th root computation, for instance as in

h'(z) = h'(z_last)*root(n, (1+z^n)/h'(z_last)^n ) .