The equation of the curve satisfying the differential equation x 2 d y = 2 - y d x and passing through P 1 , 4 is

Step-by-step solution

The given equation is d y d x = 2 - y x 2 ⇒ d y d x + y 1 x 2 = 2 x 2 Integrating factor = e ∫ d x x 2 = e - 1 x ∴ the solution is y e - 1 x = ∫ 2 x 2 e - 1 x d x Let - 1 x = t d x x 2 = d t i.e. y ⋅ e - 1 x = 2 ∫ e t d t ⇒ y e - 1 x = 2 e t + c ⇒ y e - 1 x = 2 e - 1 x + c ⇒ y = 2 + c ⋅ e 1 x Since, the curve is passing through P 1 , 4 ⇒ 2 e = c ⇒ y = 2 + 2 e ⋅ e 1 x