I have been reading the Van Der Pol article, On "Relaxations Oscilations", 1926, and i want to obtain the Van Der Pol equation from the general damped equation :
$$\dfrac{d^2x}{dt^2}-\alpha \dfrac{dx}{dt}+\omega^2x=0$$
and obtain,
$$\dfrac{d^2v}{dt^2}-\dfrac{\alpha}{\omega}(1-v^2)\dfrac{dv}{dt}+v=0\ \ \ \ \ \ \ \ \ \ (1)$$
Van Der Pol usses the equation,
$$\dfrac{d^2x}{dt^2}-(\alpha-3\gamma x^2) \dfrac{dx}{dt}+\omega^2x=0$$
and the transformation, $$\omega t=t' $$, $$x=\sqrt{\dfrac{\alpha}{3\gamma}}v$$
to do it, but i can't obtain (1) using that susbsitution, i don't get how to to change the variable of differentiation, any help? Thanks!