The solution of the differential equation d x d y = 1 + x 2 1 + y 2 is

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The solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1+y^2}{1+x^2}$ is

MathematicsDifferential EquationsMHT CETMHT CET 2023 (11 May Shift 1)

Options:

A $x+y=\mathrm{c}$, where $\mathrm{c}$ is a constant of integration.
B $x-y=\mathrm{c}(x y)$, where $\mathrm{c}$ is a constant of integration.
C $x+y=\mathrm{c}(1+x y)$, where $\mathrm{c}$ is a constant of integration.
D $y-x=\mathrm{c}(1+x y)$, where $\mathrm{c}$ is a constant of integration.

Solution:

2916 Upvotes Verified Answer

The correct answer is: $y-x=\mathrm{c}(1+x y)$, where $\mathrm{c}$ is a constant of integration.

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