Answer
$y(x)=C_1e^{3x}\cos 5x+C_2 e^{3x}\sin 5x$.
Work Step by Step
Solve the characteristic equation for the differential equation. $$r^2-6r+34=0$$
Factor and solve for the roots. $$r^2-6r+34=0$$ $$r_1=3-5i, r_2=3+5i$$
This implies that there are two independent solutions to the differential equation $y_1(x)=e^{3x}\cos 5x$ and $y_2=e^{3x}\sin 5x$.
Therefore, the general equation is equal to $y(x)=C_1e^{3x}\cos 5x+C_2 e^{3x}\sin 5x$.