Consider the nonhomogeneous systemX' =X+Find a fundamental matrix y(t) for the associated homogeneous system.Also, determine the vector u (t) satisfying the equation X(t) = 4(t) u (t)which is a particular solution of the nonhomogeneous system.3eSte7t[2e-St e2t3649O A. 4t) =; u (t)3e2test[2e-St 2t36B. (t) =est; u (t) =t +e'est36[-2e-St 2tO C. Ųut) =e-St49u (t)3e2tt +3est156[-2eSt e2t3e2t49O D. 4(t) =e-Stu (t) =

Given, the nonhomogeneous system X'=-4231X+e3te2t (1)

| 3 1 Find a fundamental matrix y(t) for the associated homogeneous system. Also, determine the vector u (t) satisfying the equation X(t) = 4(t) u (t) wwhich is a particular solution of the nonhomogeneous system. 3 eSt 36 49 [2e-st e2t 1

| 3 1 Find a fundamental matrix y(t) for the associated homogeneous system. Also, determine the vector u (t) satisfying the equation X(t) = 4(t) u (t) wwhich is a particular solution of the nonhomogeneous system. 3 eSt 36 49 [2e-st e2t 1

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

Consider the nonhomogeneous system
X' =
X+
Find a fundamental matrix y(t) for the associated homogeneous system.
Also, determine the vector u (t) satisfying the equation X(t) = 4(t) u (t)
which is a particular solution of the nonhomogeneous system.
3
eSt
e7t
[2e-St e2t
36
49
O A. 4t) =
; u (t)
3e2t
est
[2e-St 2t
36
B. (t) =
est
; u (t) =
t +e'
est
36
[-2e-St 2t
O C. Ųut) =
e-St
49
u (t)
3e2t
t +
3
est
1
56
[-2eSt e2t
3e2t
49
O D. 4(t) =
e-St
u (t) =

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