The curve satisfying the differential equation, y d x - x + 3 y 2 d y = 0 and passing through the point ( 1 , 1 ) also passes through the point

Step-by-step solution

Given differential equation, y d x - x d y - 3 y 2   d y = 0 ⇒ d x d y = x y + 3 y d x d y - x y = 3 y I.F. = e - ∫ 1 y   d y   = e - ln ⁡ y = 1 y ∴ solution is x y =   ∫ 3 y   . 1 y d y ⇒ x y = 3 y + c Passes through ( 1 , 1 ) , ∴   1 = 3 + c   ; c = - 2 Equation of required curve, x = 3 y 2 - 2 y Clearly, it passes through − 1 3 , 1 3 .