Show that `y=a e^(2x)+b e^(-x)` is a solution of the differential equation `(d^2y)/(dx^2)-((dy)/(dx))-2y=0.`

Explanation

To show that \( y = a e^{2x} + b e^{-x} \) is a solution of the differential equation

\[ \frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 0, \]

we will follow these steps:

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