Chapter 8 - Linear Differential Equations of Order n - 8.2 Constant Coefficient Homogeneous Linear Differential Equations - Problems - Page 513: 8

$y=C_1e^{2t}+C_2e^{-t}$

Solve the characteristic equation for the differential equation. $$r^2-r-2=0$$ Factor and solve for the roots. $$(r-2)(r+1)=0$$ $$r=2,-1$$ The general equation is equal to $y=C_1e^{r_1t}+C_2e^{r_2t}$. Therefore, the solution equals $y=C_1e^{2t}+C_2e^{-t}$.