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The general solution of the differential equation $(1 + y^{2}) d x + (1 + x^{2}) d y = 0$ is

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x−y=C(1−xy)

x−y=C(1+xy)

x+y=C(1−xy)

x+y=C(1+xy)

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detailed solution

Correct option is C

We have,1+y2dx+1+x2dy=0⇒dx1+x2+dy1+y2=0On integration, we get tan−1⁡x+tan−1⁡y=tan−1⁡C⇒ x+y1−xy=C⇒x+y=C(1−xy)

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The general solution of the differential equation 1+y2dx+1+x2dy=0 is

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The general solution of the differential equation $(1 + y^{2}) d x + (1 + x^{2}) d y = 0$ is