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The integrating factor of the differenti...

The integrating factor of the differential equation `(dy)/(dx)(x(log)_e x)+y=2(log)_e x` is given by

A

x

B

`e^(x)`

C

`log_(e)x`

D

`log_(e)(log_(e)x)`

Text Solution

Verified by Experts

The correct Answer is:
C
`therefore (dy)(dx)+y/(xlog_(e)x)=2/x`
`therefore` I.F. `=e^(int1/(xlog_(e)x)dx)`
`=e^(log_(e )(log_(e)x)`
`=log_(e)x`
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