Use eigenvalue metnoa to nina requirea solution of the following system. x₁ x2 = −4x₁ - 3x2 – £3 and - = 2x1 + x₂-x3 x3 = = 4x₁ +4x2+2x3. The initial conditions are ₁ (0) = 0.x₂ (0) = 1 and 3 (0) = 4. x(t) = cos 2t 6 -2 + sin 2t 6 x(t) = cos 3t 4 3 2 -2 +e² 7 2 x(t) = cos 3t -3 + sin 3t ----B-F -5 +e²t 4 -2 + sin 3t 2 2 3 -6 +e²t 3 -2 4 1 3 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Use eigenvalue metnoa to nna requirea
solution of the following system.
x₁
x2 = −4x₁3x2 – £3 and
-
x3
= 2x1 + x2 = x3
O
=
= 4x₁ + 4x2 + 2x3. The initial
conditions are ₁ (0) = 0, x2 (0) = 1
and 3 (0) = 4.
2
-8-8-0
-2 + sin 2t -2 +e² 3
7
x(t) = cos 2t
6
6
4
2
H H+O
-5 +e²t 4
3
x(t) = cos 3t -3 + sin 3t
x(t) = cos 3t
x(t) = cos 2t
2
-#-#-D
-2 + sin 3t
3
4
2
-6
-4 + sin 2t
6
3
2
tel
+ e
0
Transcribed Image Text:Use eigenvalue metnoa to nna requirea solution of the following system. x₁ x2 = −4x₁3x2 – £3 and - x3 = 2x1 + x2 = x3 O = = 4x₁ + 4x2 + 2x3. The initial conditions are ₁ (0) = 0, x2 (0) = 1 and 3 (0) = 4. 2 -8-8-0 -2 + sin 2t -2 +e² 3 7 x(t) = cos 2t 6 6 4 2 H H+O -5 +e²t 4 3 x(t) = cos 3t -3 + sin 3t x(t) = cos 3t x(t) = cos 2t 2 -#-#-D -2 + sin 3t 3 4 2 -6 -4 + sin 2t 6 3 2 tel + e 0
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