Let the solution curve of the differential equation \( x d y=\left(\sqrt{x^{2}+y^{2}}+y\right) d...

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Let the solution curve of the differential equation \( x d y=\left(\sqrt{x^{2}+y^{2}}+y\right) d x, x0 \) intersect the line \( x=1 \) at \( y=0 \) and the line \( x=2 \) at \( y=\alpha \). Then the value of \( \alpha \) is
(a) \( \frac{1}{2} \)
(b) \( \frac{3}{2} \)
(c) \( -\frac{3}{2} \)
(d) \( \frac{5}{2} \)
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