Solve \( \left(x+2 y^{2}\right) \frac{d y}{d x}=y \), given that \( x=2 \) when \( y=1 \).

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Solve \( \left(x+2 y^{2}\right) \frac{d y}{d x}=y \), given that \( x=2 \) when \( y=1 \).
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