Solution
= Solution
After division by $x>0$, the equation is linear with coefficient $-1/x$ on $y$. Its <integrating factor> is $1/x$, and the <product rule> gives
$$
\left(\frac yx\right)'=\frac{xy'-y}{x^2}=e^x\sin x.
$$
Using the <antiderivative> from the preceding part,
$$
\boxed{y(x)=Cx+\frac{xe^x}{2}(\sin x-\cos x),\qquad x>0.}
$$
The arbitrary constant multiplies the homogeneous solution $x$.