If \( x=\frac{1+\log t}{t^{2}}, y=\frac{3+2 \log t}{t}, t0 \), prov...

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If \( x=\frac{1+\log t}{t^{2}}, y=\frac{3+2 \log t}{t}, t0 \), prove that :
\[
y \frac{d y}{d x}-2 x\left(\frac{d y}{d x}\right)^{2}=1 \text {. }
\]
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