Let $$y = y(x)$$ be the solution of the differential equation $$x \, dy = (y + x^3 \cos x) \, dx$$ with $$y(\pi) = 0$$, then $$y\left(\frac{\pi}{2}\right)$$ is equal to:

A

$$\frac{\pi^2}{4} + \frac{\pi}{2}$$

B

$$\frac{\pi^2}{2} + \frac{\pi}{4}$$

C

$$\frac{\pi^2}{2} - \frac{\pi}{4}$$

D

$$\frac{\pi^2}{4} - \frac{\pi}{2}$$