10. Find the general solution of the system of differential equations3-2 -2d.X =-3 -2 -6Xdt3101+ 2tet+ 3t?et+ 4t°et31-3Hint: The characteristic polymomial of the coefficient matrix is -(A- 4)²(A- 3). Moreover(:)21Xp(t) = t²et+t³et+t'e3t-1-1-3is a particular solution of the system.

Given system of differential equation is ddtx=3-2-2-3-2-63610x+2te4t2-10+3t2e4t20-1+4t3e3t13-3…

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.

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

Section: Chapter Questions

Problem 1RQ

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Question

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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