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3. Find the general solution of the system of differential equations d X = dt 8. -5 10 cos(7t) – 7 sin(7t) ) 10 cos(7t) 7 cos(7t) + sin(7t) 10 sin(7t) ). + 4t°e7t + 8t"e7t Hint: The characteristic polynomial of the coefficient matrix is X2 14A + 98. Moreover Xp(t) = t*e7t ( cos(7t) – 7 sin(7t) 10 cos(7t)") +t 7 cos(7t) + sin(7t) 10 sin(7t) ) is a particular solution of the system.

3. Find the general solution of the system of differential equations d X = dt 8. -5 10 cos(7t) – 7 sin(7t) ) 10 cos(7t) 7 cos(7t) + sin(7t) 10 sin(7t) ). + 4t°e7t + 8t"e7t Hint: The characteristic polynomial of the coefficient matrix is X2 14A + 98. Moreover Xp(t) = t*e7t ( cos(7t) – 7 sin(7t) 10 cos(7t)") +t 7 cos(7t) + sin(7t) 10 sin(7t) ) is a particular solution of the system.

Advanced Engineering Mathematics
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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3. Find the general solution of the system of differential equations d X = dt 8. -5 10 cos(7t) – 7 sin(7t) ) 10 cos(7t) 7 cos(7t) + sin(7t) ) 10 sin(7t) + 4t3e7t + 8t"e7t Hint: The characteristic polynomial of the coefficient matrix is X? 14A + 98. Moreover cos(7t) – 7 sin(7t)+ 8e7t 10 cos(7t) ') +*( 7 cos(7t) + sin(7t) 10 sin(7t) ) Xp(t) = t*e7t is a particular solution of the system.
Transcribed Image Text:3. Find the general solution of the system of differential equations d X = dt 8. -5 10 cos(7t) – 7 sin(7t) ) 10 cos(7t) 7 cos(7t) + sin(7t) ) 10 sin(7t) + 4t3e7t + 8t"e7t Hint: The characteristic polynomial of the coefficient matrix is X? 14A + 98. Moreover cos(7t) – 7 sin(7t)+ 8e7t 10 cos(7t) ') +*( 7 cos(7t) + sin(7t) 10 sin(7t) ) Xp(t) = t*e7t is a particular solution of the system.
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