Answer
$y=- \cos x +\frac{1}{x}\sin x +\frac{C}{x}$
Work Step by Step
This is a linear equation and has the integrating factor as follows $$\alpha(x)= e^{\int P(x)dx}=e^{ \int \frac{1}{x} dx}=e^{\ln x}=x.$$
Now the general solution is
\begin{align}
y& =\alpha^{-1}(x)\left( \int\alpha(x) Q(x)dx +C\right)\\
& =\frac{1}{x}\left( -x\cos x +\sin x +C\right)\\
& =- \cos x +\frac{1}{x}\sin x +\frac{C}{x}\\
\end{align}
where we did the integration by parts.
