Verify that \( y=c e^{\tan ^{-1} x} \) is a solution of the differe...

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Verify that \( y=c e^{\tan ^{-1} x} \) is a solution of the differential equation
\( \mathrm{P} \)
\[
\left(1+x^{2}\right) \frac{d^{2} y}{d x^{2}}+(2 x-1) \frac{d y}{d x}=0
\]
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