Answer
$Solutions: r=-1,\ r=-2$
Work Step by Step
$t^2(t^r)''+4t(t^r)'+2(t^r)=0$
$t^2(r-1)rt^{r-2}+4trt^{r-1}+2t^r=0$
$[(r-1)r+4r+2]t^r=0$
$(r+1)(r+2)t^r=0$
$Solutions: r=-1,\ r=-2$
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 1 - Introduction - 1.3 Classification of Differential Equations - Problems - Page 25: 19
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