$\sin(y)+x\cos(y)y^\prime-20yy^\prime=y^\prime\ln(x)+\frac{y}{x}$

$\frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}$

$x=r\cos(\theta)=(2-\cos(\theta))\cos(\theta)$

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

$\text{Let }w=\sqrt{2x^3-4x}.$

$y^\prime=\sec(w)+x\sec(w)\tan(w)w^\prime$

What is $w′$ ? Substitute $w$ and $w′$  into the equation in Step 2.