If \( y(x) \) is the solution of the differential equation \( \frac{d y}{d x}+\left(\frac{2 x+1}...

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If \( y(x) \) is the solution of the differential equation \( \frac{d y}{d x}+\left(\frac{2 x+1}{x}\right) y=e^{-2 x}, x>0 \), where \( y(1)=\frac{1}{2} e^{-2} \), then
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