Question

Solve :

$\frac{dy}{dx}=\frac{1}{y^2+\sin y},y\ne 0$

Answer 1

$\frac{dy}{dx}=\frac{1}{y^2+\sin y}$

$\frac{dx}{dy}=y^2+\sin y$

$dx=(y^2+\sin y)dy$

Integrating both sides,

$\int dx=\int (y^2+\sin y)dy$

$x=\frac{y^3}{3}-\cos y+C$

This is the required solution.