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 - 8.1 General Theory for Linear Differential Equations - True-False Review - Page 503: b

Answer

False

Work Step by Step

Recall Theorem 6.1.5. Since, for any $x_0$ point in $I$ there will be a solution such that $W[y_1,y_2,.....y_n]=0$. This yields $(y_1,y_2,.....y_n)$ is linearly dependent on $I$. Therefore, the given statement is false.
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