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 - 8.2 Constant Coefficient Homogeneous Linear Differential Equations - Problems - Page 513: 19

Answer

$y(x)=C_1e^{7x}\cos 3x+C_2 e^{7x}\sin 3x$

Work Step by Step

Solve the characteristic equation for the differential equation. $$r^2-14r+58=0$$ Factor and solve for the roots. $r_1=7-3i; r_2=7+3i$ as roots. This implies that there are two independent solutions to the differential equation $y_1(x)=e^{7x}\sin 3x$ and $y_2= e^{7x}\cos 3x$ Therefore, the general equation is equal to $y(x)=C_1e^{7x}\cos 3x+C_2 e^{7x}\sin 3x$
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