Solving second order implicit differential equation

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Stephon Henry-Rerrie 2019 年 4 月 18 日

編集済み: David Wilson 2019 年 4 月 18 日

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 2019 年 4 月 18 日

編集済み: Torsten 2019 年 4 月 18 日

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

David Wilson 2019 年 4 月 18 日

編集済み: David Wilson 2019 年 4 月 18 日

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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