Calculating this implicit differentiation for $\frac{dy}{dx}$

Question

I'm trying to calculate this differential equation using implicit differentiation for $\frac{dy}{dx}$ in terms of x and y:

$2x^{3}y + 5x + 6y - sin(\pi y) = 8$

What I have tried:

By differentiating with respect to x

$6x^{2}y+\frac{dy}{dx}2x^{3}+5+\frac{dy}{dx}6-\frac{dy}{dx}\pi \cos(\pi y) = 0$

I'm not sure where to go from here.

Answer 1

You have already obtained a relation between $x,y,y'$. Now, you need to "solve" with respect to $y'$, getting $$ y' = \dfrac{-6x^2 y-5}{2x^3+6-\pi \cos(\pi y)}. $$