Solution
= Solution
Multiplication by the <integrating factor> and the <product rule> turn the left side into a single <derivative>:
$$
(y\sin x)'=\sin x\cos^2x.
$$
Using <integration by substitution> $u=\cos x$ gives $y\sin x=-\cos^3x/3+C$. Therefore the <general solution> is
$$
\boxed{y(x)=\frac{C-\frac13\cos^3x}{\sin x},\qquad0<x<\frac\pi2.}
$$
There is one arbitrary <constant of integration>, as expected for a first-order <ordinary differential equation>.