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If dy/dx=(xy + y)/(xy+x), then the solut...

If `dy/dx=(xy + y)/(xy+x)`, then the solution of the differential equation is (A) `y=xe^x+c ` (B) `y=e^x+c ` (C) `y=Axe^(x-y)` (D) `y=x+A`

A

`y=xe^(x)+c`

B

`y=e^(x)+c`

C

`y=x+c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`(dy)/(x)=(y(x+1))/(x(y+1))`
`int((y+1))/(y)dy = int((x+1))/(x)dx`
`int(1+(1)/(y))dy= int (1+(1)/(x))dx`
`y + ln y = x + ln x + c`
`y-x = ln (x)/(y) + c`
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