Linear Methods 5. Find the general solution of the system of differen-tial equations5 + a5+ 2ad.5+ aX -10+4adt5+ a15 + 6awhere a + -5, a # 0 is a real nonzero constant. Hint:The characteristic polynomial of the coefficient matrix is-(A – 5 – 2a)2(A – 5 + a).

Consider that the coefficient matrix is 5+α-αα-α5+αααα5+α. The eigenvalues are the roots of the…

5. Find the general solution of the system of differen- tial equations 5+a a 5+ 2a d 5+a x - 10+4a dt a 5 +a 15 + 6a where a -5, a ± 0 is a real nonzero constant. Hint: The characteristic polynomial of the coefficient matrix is -(A – 5 – 2a)²(A – 5 + a).

5. Find the general solution of the system of differen- tial equations 5+a a 5+ 2a d 5+a x - 10+4a dt a 5 +a 15 + 6a where a -5, a ± 0 is a real nonzero constant. Hint: The characteristic polynomial of the coefficient matrix is -(A – 5 – 2a)²(A – 5 + a).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Linear Methods

5. Find the general solution of the system of differen-
tial equations
5 + a
5+ 2a
d.
5+ a
X -
10+4a
dt
5+ a
15 + 6a
where a + -5, a # 0 is a real nonzero constant. Hint:
The characteristic polynomial of the coefficient matrix is
-(A – 5 – 2a)2(A – 5 + a).

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