Answer
$-e^{2t}$
Work Step by Step
$W(e^{t}sint,e^{t}cost) = |\begin{matrix}
e^{t}sint & e^{t}cost\\
e^{t}(sint+cost) & e^{t}(cost-sint)\\
\end{matrix}| = e^{2t}(sintcost-sin^{2}t)-e^{2t}(sintcost+cos^{2}t)= -e^{2t}(sin^{2}t+cos^{2}t)=-e^{2t}$
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 - 3.2 Solutions of Linear Homogenous Equations; the Wronskian - Problems - Page 155: 5
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