## Differential Equations and Linear Algebra (4th Edition)

Published by Pearson

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

#### Answer

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

#### Work Step by Step

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

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