(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to solve this differential equation numerically. I hope you can help me, it's not homework!

2. Relevant equations

This is the equation to be solved

[itex]x''=\dfrac{\alpha}{x}-\beta\dfrac{(x'-\gamma x)^2}{x}-\delta x - \dfrac{\varepsilon}{x^2}[/itex]

3. The attempt at a solution

I've tried with a simple discretization, but it doesn't seem to be stable.

[itex]\dfrac{x(i)-2x(i-1)+x(i-2)}{h^2}=\dfrac{\alpha}{x(i-1)}-\beta\dfrac{\left(\dfrac{x(i)-x(i-1)}{h}-\gamma x(i-1)\right)^2}{x(i-1)}-\delta x(i-1) - \dfrac{\varepsilon}{x(i-1)^2}[/itex]

I think it's better to use Runge-Kutta IV but I have no idea how to apply it on such a complicated equation.

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# Homework Help: Difficult non-linear differential equation

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