Non-Linear Differential Equation

Calculus Level 5

14(y)212y=y2y\large \frac{1}{4}(y')^2 - \frac{1}{2}y' = y^2 - y

The non-linear differential equation above admits two non-zero solutions y1y_1 and y2y_2. Suppose that y1(0)=y2(0)=2y_1(0) = y_2(0) = 2.

What is y1(1)+y2(1)y_1(1) + y_2(1)?

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