Prove that the general solution of the nonhomogeneous linear system, 6 x-(1-1)×(1)²² · (-)-(-) X + + t + X' = on the interval (-∞, ∞) is the following. Let X₁ 1 1 -2 1 x = √(-₁² √₂)√²+ + ₂/(₁+² √₂) ₁-√² + (1) ²2² + (-²) ₁ + (²) -1 e − 1 e-v 1 1 = (-₁ -² √₂ ) o√²², ×₂ = ( − 1 + √₂ ) e-√²¹, x₂ − (¹) ₁² + (−²)² + (1) = ¹2 t - P and A = (1-1). Then

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Prove that the general solution of the nonhomogeneous linear system,
6
x-(1-1)×(1)²² · (-)-(-)
X +
+
t +
X' =
on the interval (-∞, ∞) is the following.
Let X₁
1
1
-2
1
x = √(-₁² √₂)√²+ + ₂/(₁+² √₂) ₁-√² + (1) ²2² + (-²) ₁ + (²)
-1 e − 1 e-v
1
1
= (-₁ -² √₂ ) o√²², ×₂ = ( − 1 + √₂ ) e-√²¹, x₂ − (¹) ₁² + (−²)² + (1)
=
¹2
t
-
P
and A = (1-1). Then
Transcribed Image Text:Prove that the general solution of the nonhomogeneous linear system, 6 x-(1-1)×(1)²² · (-)-(-) X + + t + X' = on the interval (-∞, ∞) is the following. Let X₁ 1 1 -2 1 x = √(-₁² √₂)√²+ + ₂/(₁+² √₂) ₁-√² + (1) ²2² + (-²) ₁ + (²) -1 e − 1 e-v 1 1 = (-₁ -² √₂ ) o√²², ×₂ = ( − 1 + √₂ ) e-√²¹, x₂ − (¹) ₁² + (−²)² + (1) = ¹2 t - P and A = (1-1). Then
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