If for x ≥ 0 , y = y x is the solution of the differential equation, x + 1 d y = x + 1 2 + y - 3 d x , y 2 = 0 then y 3 is equal to ________

Step-by-step solution

d y d x = 1 + x + y - 3 1 + x d y d x - 1 1 + x y = 1 + x - 3 ( 1 + x ) I.F = e - ∫ 1 ( 1 + x ) d x = 1 ( 1 + x ) ∴ d d x y 1 + x = x + 3 1 + x - 1 + c ⇒ y 1 + x = x + 3 1 + x - 1 + c ⇒ y = 1 + x x + 3 ( 1 + x ) + c , ∴ at x = 2 ,   y = 0 ⇒ 0 = 3 2 + 1 + c ⇒ c = - 3 At x = 3 ,   y = 3