Step-by-Step Solution
Key Concept: Verifying a solution to a differential equation by substitution and identifying the order and number of arbitrary constants
Given $xy = ae^t + be^{-t}$ where $t$ is the independent variable, we differentiate to find $\frac{dy}{dx} = ue^t - be^{-t}$. Computing the second derivative and substituting into the differential equation $x\frac{d^2y}{dx^2} + 2\frac{dy}{dx} - xy = 0$ confirms the solution satisfies the equation. The general solution involves two arbitrary constants $a$ and $b$, making this a second-order linear differential equation.
Correct Answer: 1