9. Find the general solution of the system of differential equations2 2 1d25 21 2 2(;)()1+ 6t°e+ 7t°e*+ 8t°e7+1Hint: The characteristic polyomial of the coefficient matrix is -(A-1)2(A- 7). Moreover21u,(t) = t®e?+t'e+ te7t21is a particular solution of the system.

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2 2 1 2 5 2 1 2 2 dt 2 (3) 1 + 6t°e + 7t°e? -1 -1 + 8t'et 1 Hint: The characteristic polymomial of the coefficient matrix is -(A-1)2(A- 7). Moreover 1 u,(t) = t®e' +t'e + t°e7t 1 is a particular solution of the system.

2 2 1 2 5 2 1 2 2 dt 2 (3) 1 + 6t°e + 7t°e? -1 -1 + 8t'et 1 Hint: The characteristic polymomial of the coefficient matrix is -(A-1)2(A- 7). Moreover 1 u,(t) = t®e' +t'e + t°e7t 1 is a particular solution of the system.

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

9. Find the general solution of the system of differential equations
2 2 1
d
25 2
1 2 2
(;)
()
1
+ 6t°e
+ 7t°e*
+ 8t°e7+
1
Hint: The characteristic polyomial of the coefficient matrix is -(A-1)2(A- 7). Moreover
2
1
u,(t) = t®e?
+t'e
+ te7t
2
1
is a particular solution of the system.

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