Which differential equation does the family $y = Ae^{x} + Be^{-2x}$ satisfy, $A, B$ being arbitrary constants?

Explanation

1. 01

   There are two constants, so differentiate twice and eliminate them.

2. 02

   Eliminating gives $\frac{d^2y}{dx^2} + \frac{dy}{dx} - 2y = 0$, of order 2.