Solving second order implicit differential equation

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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!
  1 Comment
Torsten
Torsten on 18 Apr 2019
Edited: Torsten on 18 Apr 2019
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

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Accepted Answer

David Wilson
David Wilson on 18 Apr 2019
Edited: David Wilson on 18 Apr 2019
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.

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