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Solving second order implicit differential equation

Asked by Stephon Henry-Rerrie on 18 Apr 2019
Latest activity Edited by David Wilson on 18 Apr 2019
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

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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1 Answer

Answer by David Wilson on 18 Apr 2019
Edited by David Wilson on 18 Apr 2019
 Accepted Answer

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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