Question

The solution of the equation `dx/dy - x = y + 1` is ______

पर्याय

• x = ce^y - y - 2

• y = x + ce^y - 2

• x + ce^y + y - 2 = 0

• x - ce^y + y - 2 = 0

Answer 1

The solution of the equation `dx/dy - x = y + 1` is x = ce^y - y - 2

Explanation:

`dx/dy - x = y + 1`

∴ I.F. = `e^{int-1  dy} = e^-y`

∴ solution of the given equation is

`x.e^-y = int(y + 1)e^-y dy + c`

⇒ `xe^-y = e^-y(-y - 2) + c`

⇒ `x = ce^-y - y - 2`