Answer
$\{e^{3x}\cos 4x, e^{3x}\sin 4x\}$
Work Step by Step
Solve the characteristic equation for the differential equation. $$r^2-6r+25=0$$
Factor and solve for the roots. $$r_1=3-4i, r_2=3+4i$$
The general equation is equal to $y=C_1e^{3x}cos 4x+C_2e^{3x}\sin 4x$
Therefore, $\{e^{3x}\cos 4x, e^{3x}\sin 4x\}$ is a basis for the solution space.