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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