Verify that the vector Xp is a particular solution of the given nonhomogeneous linear system. dx dt dy - (-₁) ₁ + (₁) t dt Writing the system in the form X' = AX + F for some coefficient matrix A and vector F, one obtains the following. X'= For Xp 1 3 = x + 4y + 2t - 9 = 3x + 2y — 4t - 24; X = 4 X₂' 2 = ·(-²) ₁ + (1). 2 2 X + t one has 2 -4 + -9 -24
Verify that the vector Xp is a particular solution of the given nonhomogeneous linear system. dx dt dy - (-₁) ₁ + (₁) t dt Writing the system in the form X' = AX + F for some coefficient matrix A and vector F, one obtains the following. X'= For Xp 1 3 = x + 4y + 2t - 9 = 3x + 2y — 4t - 24; X = 4 X₂' 2 = ·(-²) ₁ + (1). 2 2 X + t one has 2 -4 + -9 -24
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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Why does it mark me wrong on X prime? Please help
Transcribed Image Text:Verify that the vector Xp is a particular solution of the given nonhomogeneous linear system.
dx
dt
dy
L = 3x + 2y − 4t - 24; X₁ = (-²)t +
-(-³)₁ + (²)
dt
Writing the system in the form X' = AX + F for some coefficient matrix A and vector F, one obtains the following.
X'=
For Xp
1
3
= x + 4y + 2t - 9
AXp
2
9×8·3
X + t
-4
X₂'
=
= (-²)² + (²)
4
+ F =
2
2
2
one has
-1
Since the above expressions are equal
+
-9
-24
~~~ ·x₂ - (-²) ₁ + (²)
=
is a particular solution of the given system.
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