Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 8 - Linear Differential Equations of Order n - 8.2 Constant Coefficient Homogeneous Linear Differential Equations - Problems: 9

Answer

$y=C_1e^{3t}+C_2te^{3t}$

Work Step by Step

Solve the characteristic equation for the differential equation. $$r^2-6r-9=0$$ Factor and solve for the roots. $$(r-3)(r-3)=0$$ $$r=3,3$$ The general equation for repeated roots is equal to $y=C_1e^{r_1t}+C_2te^{r_1t}$. Therefore, the solution equals $y=C_1e^{3t}+C_2te^{3t}$.
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