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$\large \frac{1}{4}(y')^2 - \frac{1}{2}y' = y^2 - y$

The non-linear differential equation above admits two non-zero solutions $y_1$ and $y_2$. Suppose that $y_1(0) = y_2(0) = 2$.

What is $y_1(1) + y_2(1)$?

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