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

Question

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

MARKS App · Accepted Answer

2 x y d y d x = y 2 + x ln ⁡ x 2 y d y d x - y 2 x = ln ⁡ x Put, y 2 = t ⇒ 2 y d y d x = d t d x d t d x - t x = ln ⁡ x I.F. = e ∫ - 1 x d x = e - l n x = 1 x The solution is t x = ∫ ln ⁡ x x d x t x = ln ⁡ x 2 2 + c y 2 x = ln ⁡ x 2 2 + c 2 y 2 = x ln ⁡ x 2 + 2 c x

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