Answer
$y(x)=C_1e^{7x}\cos 3x+C_2 e^{7x}\sin 3x$
Work Step by Step
Solve the characteristic equation for the differential equation. $$r^2-14r+58=0$$
Factor and solve for the roots. $r_1=7-3i; r_2=7+3i$ as roots.
This implies that there are two independent solutions to the differential equation $y_1(x)=e^{7x}\sin 3x$ and $y_2= e^{7x}\cos 3x$
Therefore, the general equation is equal to $y(x)=C_1e^{7x}\cos 3x+C_2 e^{7x}\sin 3x$