Question

The integrating factor of the differential equation `(x+2y^2) dy/dx = y  (y>0)` is ______.

विकल्प

• `1/x`

• x

• y

• `1/y`

Answer 1

The integrating factor of the differential equation `(x+2y^2) dy/dx = y  (y>0)` is `underlinebb(1/y)`.

Explanation:

Differential Eqn. `(x+2y^2) dy/dx = y` find, I.F.

⇒ `dy/dx = y/(x+2y^2)`

⇒ `dx/dy = (x+2y^2)/y`

⇒ `dx/dy = x/y + 2y`

As we know that

⇒ `dx/dy - x/y = 2y`

`dx/dy + Px = Q, P = (-1)/y, Q=2y`

I.F. = `e^(intpdy)`

`= e^(int-1/ydy) = e^(-logy) = 1/y`

I.F. = `1/y`