The general solution of the differential equation y 2 - x 3 d x - x y d y = 0 , x ≠ 0 is (where c is a constant of integration)

Question

The general solution of the differential equation y 2 - x 3 d x - x y d y = 0 , x ≠ 0 is (where c is a constant of integration), y 2 + 2 x 2 + c x 3 = 0, y 2 - 2 x 2 + c x 3 = 0, y 2 - 2 x 3 + c x 2 = 0, y 2 + 2 x 3 + c x 2 = 0

MARKS App · Accepted Answer

Given differential equation can be written as: y 2 d x - x y d y = x 3 d x ⇒ y d x - x d y = x 3 y d x ⇒ y d x - x d y y 2 = x y 3 d x ⇒ ∫ d x y x y 3 = ∫ d x ⇒ x y - 3 + 1 - 3 + 1 = x + c ⇒ y 2 = - 2 x 3 - c x 2 ⇒ y 2 + 2 x 3 + c x 2 = 0

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