Let the solution curve of the differential equation x d y d x - y = y 2 + 16 x 2 , y 1 = 3 be y = y x . Then y 2 is equal to

Step-by-step solution

Given, x d y d x - y = y 2 + 16 x 2 ⇒   d y d x = y 2 + 16 x 2 + y x Let y = x t ⇒ d y d x = x d t d x + t ⇒ x d t d x + t = t + t 2 + 16 ⇒ d t t 2 + 16 = d x x Now integrating both side we get, ⇒ ∫ d t t 2 + 16 = ∫ d x x ⇒   ln t + t 2 + 16 = ln x + ln c ⇒   y x + y 2 + 16 x 2 x = c x ∵       y 1 = 3 so ⇒   3 1 + 3 2 + 16 × 1 2 1 = c × 1 ⇒ c = 8 So solution becomes, y x + y 2 + 16 x 2 x = 8 x Now y