Let y = f ( x ) be the solution of the differential equation y ( x + 1 ) d x - x 2 d y = 0 , y ( 1 ) = e . Then lim x → 0 + f ( x ) is equal to

Step-by-step solution

Given, y ( x + 1 ) d x - x 2 d y = 0 ⇒ x + 1 x 2 d x = d y y ⇒ 1 x + 1 x 2 d x = d y y Now integrating both side we get, log e x - 1 x = log e y + c Now on using y 1 = e we get, c = - 2 So, the equation of curve becomes log e x - 1 x = log e y - 2 ⇒ y = e ln x - 1 x + 2 Hence, lim x → 0 + e ln x - 1 - 1 x + 2 = e - ∞ = 0 .