# Example

Here is an important thing to consider. If $L(y) = Ay'' + By' + Cy$, that means it's a linear function, because nothing's squared. Because it's linear, we can say $L(y_1 + y_2) = L(y_1) + L(y_2)$. Also $L(cy_1) = cL(y_1)$. By this same principle if $L(y_1) = 0$ and $L(y_2) = 0$, then $L(c_1y_1 + c_2y_2) = 0$. Therefore, our final solution is $$\boxed{c_1e^{-2x} + c_2e^{5x}}$$

# Example 2- Imaginary

David Witten