The solution of the differential equation y d x - x d y x y = x d x + y d y is (where, C is an arbitrary constant)

Question

The solution of the differential equation y d x - x d y x y = x d x + y d y is (where, C is an arbitrary constant), x y = x + y + C, x y = x 2 + y 2 2 + C, ln ⁡ x y = x 2 + y 2 + C, 2 ln ⁡ x y = x 2 + y 2 + C

MARKS App · Accepted Answer

The given equation is 1 x y ⋅ y d x - x d y y 2 = x d x + y d y or d ln ⁡ x y = x d x + y d y On integrating, we get, ∫ d ln ⁡ x y = ∫ x d x + ∫ y d y ⇒ ln ⁡ x y = x 2 2 + y 2 2 + k ⇒ 2 ln ⁡ x y = x 2 + y 2 + C

Search any question & find its solution

Looking for more such questions to practice?