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Let y(x) be the solution of the differen...

Let y(x) be the solution of the differential equation `(xlogx)(dy)/(dx)+y=2xlogx, (xge1)`, Then y(e) is equal to

A

e

B

0

C

2

D

2e

Text Solution

Verified by Experts

The correct Answer is:
C
We have `(dy)/(dx) + y/(xlogx)=2`
`I.F. = e^(int1/(xlogx)dx)=e^(log(logx))=logx`
Now solution, is
`y(logx)=int2(logx)dx`
`rArr y(logx)=2[xlogx-x]+c`
When x=1, c=2.
When `x=e` then
`y=2(e-e)+2`
or y=2
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