# Non-Linear Differential Equation

Calculus Level 4

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

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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