If y = y x is the solution of the differential equation 2 x 2 d y d x - 2 x y + 3 y 2 = 0 such that y e = e 3 , then y 1 is equal to

Step-by-step solution

Given 2 x 2 d y d x - 2 x y + 3 y 2 = 0 Dividing by 2 x 2 y 2 , we get, - 1 y 2 d y d x + 1 x y = 3 2 x 2 Let 1 y = p , - 1 y 2 d y d x = d p d x ⇒    d p d x + 1 x p = 3 2 x 2 General solution will be p · e ∫ 1 x d x = ∫ 3 2 x 2 · e ∫ 1 x d x d x + c ⇒     x y = ∫ 3 2 x d x + c     ⇒ x y = 3 2   ln x + c ∵       y e = e 3 ⇒ c = 3 2         ⇒ x y = 3 2 ln x + 3 2 is the particu