Introduction : Van Der Val ODE is a second order differential equation. To analyse it's solution behaviour First we convert it into a system of first order ODEs then obtained Linearization about it's equilibrium point and phase portrait of the system.
Question : Let Van Der Pol ODE
\[\frac{d^2y}{{\rm dt}^2}+\left(y^2-1\right)\frac{dy}{dt}+y=0\ ]
Find a linearization about equilibrium point and plot the phase portrait then determine long term behaviour of the solution.
Solution :
