The solution of the differential equation 2 x e x d y + e x y d x = x sin x d x is (where, c is an arbitrary constant)

Question

The solution of the differential equation 2 x e x d y + e x y d x = x sin x d x is (where, c is an arbitrary constant), 2 y e x + sin ⁡ x = c, y sin ⁡ x = e x + c, y e x + sin ⁡ x = c, 2 y e x + cos ⁡ x = c

MARKS App · Accepted Answer

The given equation is e x ⋅ d y + e x 2 x d x ⋅ y = sin x 2 d x or d e x y = 1 2 sin ⁡ x d x On integrating, we get, e x ⋅ y = − cos x 2 + c ' i.e. 2 y e x + cos ⁡ x = c

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