Answer
$y(x)=C_1e^{-x}+C_2e^{5x}$
Work Step by Step
Solve the characteristic equation for the differential equation. $$(D+1)(D-5)y=0$$
Factor and solve for the roots. $$(r+1)(r-5)=0$$ $$r_1=-1, r_2=5$$
This implies that there are two independent solutions to the differential equation $y_1(x)=e^{-x}$ and $y_2=e^{5x}$.
Therefore, the general equation is equal to $y(x)=C_1e^{-x}+C_2e^{5x}$.