If y = f x satisfies the differential equation d y d x + 2 x 1 + x 2 y = 3 x 2 1 + x 2 where f 1 = 1 , then f 2 is equal to

Step-by-step solution

The given differential equation is a linear differential equation. Integrating factor = e ∫ 2 x 1 + x 2 d x = 1 + x 2 The solution of the differential equation is y 1 + x 2 = ∫ 3 x 2 d x = x 3 + C ∵ y 1 = 1 ⇒ C = 1 Hence, y = f x = x 3 + 1 x 2 + 1 So, f 2 = 9 5 = 1 . 8