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