Consider the nonhomogeneous system Find a fundamental matrix (t) for the associated homogeneous system. Also, determine the vector u (t) satisfying the equation X(t) = (t) u (t) which is a particular solution of the nonhomogeneous system. A. (t) = B. (t) = C. (t) = D. (t) = 2e-te-3t -e-3t et -2e-t et 31] : 2e-t et -e-3t e-3t -2e-te-3t -e-3t -e-3t] e-3t ; u (t) = u (t) = ↑ (t): ; u(t)= 2,7t et-1/e²t et + 1/e²t -est et - 1/²t + e2t ×-|-12 -2 -5 X+

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the nonhomogeneous system
1 4
X'
X+
-2 -5
Find a fundamental matrix 4(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.
1 5t
2et e-3t
A. W(t) =
(t)
est
t
-2et
B. 4(t) =
et
e3t
(t) =
e3t
27t +
e2t
-2et
C. W(t) =
e-3t
;u (t) =
e3t
7t
et
e2t
2et e3t
D. 4(t) = |
;u (t) =
e-3t
국et + e2t
Transcribed Image Text:Consider the nonhomogeneous system 1 4 X' X+ -2 -5 Find a fundamental matrix 4(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. 1 5t 2et e-3t A. W(t) = (t) est t -2et B. 4(t) = et e3t (t) = e3t 27t + e2t -2et C. W(t) = e-3t ;u (t) = e3t 7t et e2t 2et e3t D. 4(t) = | ;u (t) = e-3t 국et + e2t
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