Answer
$y(x)=C_1 e^{-7x}+C_2 e^{-5x}+C_3 e^{19x}$
Work Step by Step
Solve the auxiliary equation for the differential equation. $$r^3-7r^2-193r-665=0$$
Factor and solve for the roots. $$(r+5)(r+7)(r-19)=0$$
Roots are: $r_1=-7, r_2=-5; r_3=19$
This implies that there are $\bf{3}$ independent solutions to the differential equation and the general equation is equal to $y(x)=C_1 e^{-7x}+C_2 e^{-5x}+C_3 e^{19x}$
