Answer:
Option C
Explanation:
Given differentail equation is
(xlogx)dydx+y=2xlogx,
⇒ dydx+yxlogx=2
This is a linear differential equation.
∴ IF=e∫1xlogxdx=elog(logx)=logx
Now, the solution of given differential equation is given by
y.logx=∫logx.2dx
⇒y.logx=2∫logx.dx
⇒y.logx=2[xlogx−x]+c
At X=1, c=2
⇒ y.logx=2[xlogx−x]+2
At x=e,
y= 2(e-e)+2 ⇒y=2