Solving second order implicit differential equation

I have a differential equation that I would like to solve and it has the form: . How would people recommend I solve this numerically? Thanks!

[Torsten]

Hopefully you don't have an initial condition at z=0 ?!

Otherwise, substitute

w(z) = y(ln(z))

first.

https://de.wikipedia.org/wiki/Eulersche_Differentialgleichung

Answer 1

[David Wilson]

Just convert the 2nd order ODE into Cauchy form. You will of course need 2 initial condtions.

Define x, now you original equation is re-written as

, so that means your system of 1st order ODEs is now

Of course we will need to know the form of f(z) to solve.