Answer
$y(x)=C_1e^{x}+C_2 \cos x+C_3 \sin x$
Work Step by Step
Solve the characteristic equation for the differential equation. $$r^3-r^2+r-1=0$$
Factor and solve for the roots. $$(r-1)(r^2+1)=0$$ $$r_1=1, r_2=-i; r_3=i$$ as roots.
This implies that there are two independent solutions to the differential equation $y_1(x)=e^{x}$ and $y_2= \cos x$ and $y_3=\sin x$
Therefore, the general equation is equal to $y(x)=C_1e^{x}+C_2 \cos x+C_3 \sin x$
