Answer
$y = C_1 e^{-2t} + C_2 e^{4t}$
Work Step by Step
$y''+2y'-8y = 0$ has characteristic equation $r^2 +2r -8 = 0$
Completing the square:
$(r+1)^2 = 9 \to r=-2,4$
$y = C_1 e^{-2t} + C_2 e^{4t}$
Elementary Differential Equations and Boundary Value Problems 9th Edition
by Boyce, William E.; DiPrima, Richard C.
Published by
Wiley
ISBN 10:
0-47038-334-8
ISBN 13:
978-0-47038-334-6
Chapter 3 - Second Order Linear Equations - 3.3 Complex Roots of the Characteristic Equation - Problems - Page 163: 9
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