Question

Solve :

$si{n}^{3}x\frac{dx}{dy}=\sin y$

Answer 1

$si{n}^{3}x\frac{dx}{dy}=\sin y$

$si{n}^{3}xdx=\sin ydy$

$\int si{n}^{3}xdx=\sin ydy$

$\int \frac{3\sin x-\sin 3x}{4}dx=\int \sin ydy$

$-\frac{3}{4}\cos x+\frac{1}{12}\cos 3x=-\cos y+C$

$\cos y-\frac{3}{4}\cos x+\frac{1}{12}\cos 3x=C$ is the required solution.