Question

General solution of differential equation dy/dx= 3x^3/y-siny

Answer 1

\[\frac{dy}{dx}=\frac{3x^2}{y-\sin y}~~\text{or}~~\frac{dy}{dx}=\frac{3x^3}{y}-\sin y~~?\]

Answer 2

I hope it's the first one... The first eq is separable:
\[(y-\sin y)~dy=3x^3~dx\]
Integrating gives
\[\frac{1}{2}y^2-\cos y=\frac{3}{4}x^4+C\]