Solve the following differential equation: `xcosy\ dy=(x e^xlogx+e^x)dx`

Explanation

$$
\begin{aligned}
&x \cos y d y=\left(x e^{x} \log x+e^{x}\right) d x \\
&\int \cos y d y=\int \frac{x e^{x} \log x+e^{x}}{x} d x \\
&=\int e^{x} \log x d x+\int \frac{e^{x} d x}{x} \\
&=\int e^{x} \log x d x \\
&=e^{x} \log x=\int \frac{e^{x}}{x} d x \\
&\sin y=e^{x} \log x-\int \frac{e^{x}}{x} d x+\int \frac{e^{x}}{x} d x \\
...