Question

Solution of the equation `dy/dx + y/(x + logy) = 0` is ______ 

Options

• xy + y log y = c

• xy + y log y - y = c

• xy + log y - x = c

• xy + log y + x = c

Answer 1

Solution of the equation `dy/dx + y/(x + logy) = 0` is xy + y log y - y = c

Explanation:

`dy/dx + y/(x + logy) = 0`

⇒ `dx/dy = -(x + logy)/y`

⇒ `dx/dy + x/y = -(logy)/y`

∴ I.F. = `e^{int1/ydy} = e^{logy} = y`

∴ solution of the given equation is

x.y = `-inty. (logy dy)/y + c`

⇒ xy = -(y log y - y) + c

⇒ xy + (y log y - y) = c