Show that \( y=\frac{c-x}{1+c x}, c \) is arbitrary constant, is a solution of the differential ...

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Show that \( y=\frac{c-x}{1+c x}, c \) is arbitrary constant, is a solution of the differential equation
\[
\left(1+x^{2}\right) \frac{d y}{d x}+\left(1+y^{2}\right)=0
\]
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