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Q.The solution of the differential equation dydx=y(x+y)x(x−y)\dfrac{dy}{dx} = \dfrac{y(x + y)}{x(x - y)} is

a
log⁡∣x2−y2∣=C+2tan⁡−1(y/x)\log|x^2 - y^2| = C + 2 \tan^{-1}(y/x)
b
log⁡∣x2+y2∣=C+2tan⁡−1(y/x)\log|x^2 + y^2| = C + 2 \tan^{-1}(y/x)
c
log⁡∣xy∣=C+tan⁡−1(y/x)\log|xy| = C + \tan^{-1}(y/x)
d
x2+y2=Cx^2 + y^2 = C

Correct Answer: Option A

The correct solution involves applying the fundamental concept to derive the final value step by step...

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