10. Find the general solution of the system of differential equations d 3 -2 -2 -3 -2 -6 dt 10 2 2 1 + 2te“ + 3tet + 4t°e* -3 Hint: The characteristic polynomial of the coefficient matrix is -(A– 4)²(A – 3). Moreover 2 1 Xp(t) = t²e" + t®e4t +t*e3t -1 -3 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
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10. Find the general solution of the system of differential equations
3
-2 -2
d.
X =
-3 -2 -6
X
dt
3
10
1
+ 2tet
+ 3t?et
+ 4t°et
3
1
-3
Hint: The characteristic polymomial of the coefficient matrix is -(A- 4)²(A- 3). Moreover
(:)
2
1
Xp(t) = t²et
+t³et
+t'e3t
-1
-1
-3
is a particular solution of the system.
Transcribed Image Text:10. Find the general solution of the system of differential equations 3 -2 -2 d. X = -3 -2 -6 X dt 3 10 1 + 2tet + 3t?et + 4t°et 3 1 -3 Hint: The characteristic polymomial of the coefficient matrix is -(A- 4)²(A- 3). Moreover (:) 2 1 Xp(t) = t²et +t³et +t'e3t -1 -1 -3 is a particular solution of the system.
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