Verify that \( A x^{2}+B y^{2}=1 \) is a solution of the differenti...

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Verify that \( A x^{2}+B y^{2}=1 \) is a solution of the differential equation
\( \mathrm{P} \)
\[
x\left\{y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right\}=y \frac{d y}{d x} \text {. }
\]
W
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