Answer
$\{\cos 2x, \sin 2x\}$ is a basis for the solution space.
Work Step by Step
Solve the characteristic equation for the differential equation. $$r^2+4=0$$
Factor and solve for the roots. $$r_1=2 i, r_2=-2 i$$
The general equation is equal to $y=C_1cos 2x+C_2\sin 2x$
Therefore, $\{\cos 2x, \sin 2x\}$ is a basis for the solution space.