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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Consider the nonlinear differential equation (-2(x – y)² + v°) 2 -2 + 1 + =:A whose right hand side is written as the sum of the linear part with coefficient matrix A and a nonlinearity. (i) Show that (x*, y*) := (0, 0) is the only equilibrium. (ii) Calculate the real Jordan normal form of the coefficient matrix A using an invertible transformation matrix T E R²×2. (iii) Explain why the equilibrium (x*, y*) = (0,0) is repulsive.
Consider the nonhomogeneous system X' = X+ 3 1 Find a fundamental matrix (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 O A. 4(t) = 15 -2et ;u (t) : 3et est 1 e4t 2et 4t 3et 15 B. W(t) = ;u (t) = -e 1. est 25 1 t- e-6t et O C. 4(t) = e4t 2et (t) -3et eSt e-6t eft D. 4(t) = -2et e4t 3et ;u (t) jet + eSt 25
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