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The solution of (y(1+x^(-1))+siny)dx +(x...

The solution of `(y(1+x^(-1))+siny)dx +(x+log x +x cos y)dy=0` is

A

`(1 + y^(-1) sin y) + x^(-1) log x = c`

B

`(y+sin y)+xy log x =C`

C

`xy + y log x + x sin y = C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
The given equation can be written as
`y(1+x^(-1))dx + (x+ log x) dy + sin y dx + x cos y dy = 0`
`rArr" "d(y(x+ log x)) + d(x sin y) = 0`
`rArr" "y(x + log x)+ x sin y = C`
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