The general solution of the differential equation $\left(1+y^{2}\right) d x+\left(1+x^{2}\right) d y=0$ is
The general solution of the differential equation $\left(1+y^{2}\right) d x+\left(1+x^{2}\right) d y=0$ is
$x-y=C(1-x y)$
$x-y=C(1+x y)$
$x+y=C(1-x y)$
$x+y=C(1+x y)$
Solution
$\left(1+y^{2}\right) d x+\left(1+x^{2}\right) d y=0$ $\Rightarrow \frac{d x}{1+x^{2}}+\frac{d y}{1+y^{2}}=0$
On integrating, we get
$\begin{array}{l}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} C \\
\Rightarrow \frac{x+y}{1-x y}=C \\
\Rightarrow x+y=C(1-x y)
\end{array}$