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

Question

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

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Answer

(b) : $\frac{d y}{d x}=\frac{1+y^2}{1+x^2} \Rightarrow \frac{d y}{1+y^2}=\frac{d x}{1+x^2}$
On integrating both sides, we get
$
\tan ^{-1} y=\tan ^{-1} x+c \Rightarrow \tan ^{-1} y-\tan ^{-1} x=c
$

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