Solve the following differential equation: `(dy)/(dx)=(1+x^2)(1+y^2)`

Explanation

`
\begin{aligned}
&\frac{d y}{d x}=\frac{\left(1+y^{2}\right)}{\left(1+x^{2}\right)} \\
&\Rightarrow \int \frac{d y}{1+y^{2}}=\int \frac{d x}{1+x^{2}}+c_{1} \\
&\Rightarrow \tan ^{-1} y=\tan ^{-1} x+c_{1} \\
&\Rightarrow \tan ^{-1}\left(\frac{y-x}{1+x y}\right)=c_{1} \\
&\Rightarrow \tan c_{1}=\left(\frac{y-x}{1+x y}\right) \\
&\text { let } \tan c_{1}=c \\
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