Solving second order implicit differential equation

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Stephon Henry-Rerrie
编辑： David Wilson 2019-4-18
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!
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Torsten
Torsten 2019-4-18
编辑：Torsten 2019-4-18
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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David Wilson
David Wilson 2019-4-18
编辑：David Wilson 2019-4-18
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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