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

Question

The solution of the differential equation x d y d x = y ln ⁡ y 2 x 2 is (where, c is an arbitrary constant), y = x . e c x + 1, y = x . e c x - 1, y = x 2 . e c x + 1, y = x . e c x 2 + 1 2

MARKS App · Accepted Answer

Putting y = x v and d y d x = v + x d v d x So, v + x d v d x = 2 v ln ⁡ v ⇒ ∫ d x x = ∫ d v v ( 2 ln ⁡ v - 1 ) On integrating, we get, y = x ⋅ e c x 2 + 1 2

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