Consider the forced Van der Pol oscillator equation:
$$\huge\bf\sf \ddot x-\mu(1-x^2)\dot x+x\quad=\quad A \sin(\omega t)$$
1. Express the equation as a system of differential equations.

Question

Consider the forced Van der Pol oscillator equation:
$$\huge\bf\sf \ddot x-\mu(1-x^2)\dot x+x\quad=\quad A \sin(\omega t)$$
1. Express the equation as a system of differential equations.

zepdrix · Answer

WUT? D: HOW?

zepdrix · Answer

I only see one independent variable.
Am I trying to write it as a sytem of `x` and `t` maybe?

Hmmm this is weird..

abb0t · Answer

@shamil98

shamil98 · Answer

@abb0t  I don't know this stuff. Why don't you show us your brilliance? hm?

zepdrix · Answer

lol XD

zepdrix · Answer

I don't need to solve it or anything :d
I'm using approximation methods and computers for that.

Just trying to figure out what the "system" should look like.. hmm

anonymous · Answer

Set $y_1=x$ and $y_2=x'$, so that you see that $y_1'=y_2$ and $y_2'=x''$.

So then your original equation can be written as
$$y_2'-\mu(1-y_1^2)+y_1=A\sin\omega t$$
and you have the system
$$\begin{cases}y_1'=y_2\y_2'=\mu(1-y_1)^2-y_1+A\sin\omega t\end{cases}$$

zepdrix · Answer

Ooo nice :D thanks