Answer
$\{e^{2x}, e^{-x}\}$
Work Step by Step
Solve the characteristic equation for the differential equation. $$r^2-r-2=0$$
Factor and solve for the roots. $$(r-2) (r+1)=0 $$ $$r=2, -1$$
The general equation is equal to $y=C_1 e^{2x}+C_2 e^{-x}$
Therefore, $\{e^{2x}, e^{-x}\}$ is a basis for the solution space.