Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 17 - Second-Order Differential Equations - Review - Exercises - Page 1221: 15


Does not have any solution.

Work Step by Step

As we are given that $y''+4y'+29y=0$, $y(0)=1$ and $y(\pi)=-1$ The roots are complex numbers such as $\alpha \pm i \beta$, thus the general solution is of the form $y=e^{\alpha x}[c_1cos(\beta x)+c_2sin(\beta x)]$ From the given values, $y(0)=1$ and $y(\pi)=-1$, we get $y(0)=1$ $$y(\pi)=-e^{-2\pi}\ne -1$$ This shows that the second boundary condition cannot be satisfied , hence the given problem does not have any solution.
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