JEE Math Practice Question

Let $$y=y(x)$$ be the solution of the differential equation $$x{\log _e}x{{dy} \over {dx}} + y = {x^2}{\log _e}x,(x > 1)$$. If $$y(2) = 2$$, then $$y(e)$$ is equal to

1. A.$${{1 + {e^2}} \over 2}$$
2. B.$${{1 + {e^2}} \over 4}$$
3. C.$${{2 + {e^2}} \over 2}$$
4. D.$${{4 + {e^2}} \over 4}$$