Solution
= Solution
For the <linear differential operator> $L=(D-\alpha)(D-\beta)$, the <exponential function> is an <eigenfunction>: $Le^{\epsilon x}=(\epsilon-\alpha)(\epsilon-\beta)e^{\epsilon x}$. Distinct $\alpha,\beta$ give the two <homogeneous solutions>, while the <method of undetermined coefficients> supplies a particular solution at the distinct forcing exponent $\gamma$:
$$
\boxed{y=C_1e^{\alpha x}+C_2e^{\beta x}+\frac{k e^{\gamma x}}{(\gamma-\alpha)(\gamma-\beta)}.}
$$