My question is about whether it's possible to use the Euler Forward or 4th order Runge-Kutta Methods to approximate the following system ( where the differential of other equations are on the right hand side) :(adsbygoogle = window.adsbygoogle || []).push({});

$$

\begin{cases}

\frac{dy_1}{dt} = f_1(y_1,y_2,y'_2, ... , y_n, y'_n, t) \\

\frac{dy_2}{dt} = f_2(y_1,y'_1,y_2, ... , y_n, y'_n, t) \\

...\\

\frac{dy_n}{dt} = f_n(y_1,y'_1, ... , y_{n-1}, y'_{n-1}, y_n, t) \\

\end{cases}

$$

I know you can do it for the normal form: ## \frac{d^{(n)}y}{dt^{(n)}} = f(y, y', y'', ... , y^{(n)}, t) ## and it's also possible to analytically solve differential equations of that form using linear algebra, but I'm not sure when it's not in the normal form.

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# Approximating System of ODE's

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