Transfer the following differential equation: y" + 3y" + 2y' —- 5y = t² + e-4t cos t into a system of first order differential equations in the form of x' = A + g(t) What are , A, and ģ(t)? x(t) = = x₁ (t) x₂ (t) x3 (t) x₁ (t) x (t) = x₂(t) _x3 (t) x₁ (t)] x(t) = x₂(t) [x3 (t). x₁ (t) x(t) = | x₂ (t) x3 (t) = = = Y y' = [] " Y y' y' A = " A = " A = --- 0 0 5 1 0 5 1 0 0 1 -2 -3 0 A = 0 -3 1 1 0 1 -2 0 1 0 0 0 1 -5 2 3 -3 1 0 -2 0 1 5 > " 2 g(t) g(t) g(t) 1 = = 0 0 t² + e-4t cos(t). -4t --[ g(t) = 0 0 -4t + e t² cos(t) t² + e cos(t) 0 0 -4t cos(t)]
Transfer the following differential equation: y" + 3y" + 2y' —- 5y = t² + e-4t cos t into a system of first order differential equations in the form of x' = A + g(t) What are , A, and ģ(t)? x(t) = = x₁ (t) x₂ (t) x3 (t) x₁ (t) x (t) = x₂(t) _x3 (t) x₁ (t)] x(t) = x₂(t) [x3 (t). x₁ (t) x(t) = | x₂ (t) x3 (t) = = = Y y' = [] " Y y' y' A = " A = " A = --- 0 0 5 1 0 5 1 0 0 1 -2 -3 0 A = 0 -3 1 1 0 1 -2 0 1 0 0 0 1 -5 2 3 -3 1 0 -2 0 1 5 > " 2 g(t) g(t) g(t) 1 = = 0 0 t² + e-4t cos(t). -4t --[ g(t) = 0 0 -4t + e t² cos(t) t² + e cos(t) 0 0 -4t cos(t)]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Transfer the following differential equation:
- 4t
y" + 3y" + 2y' — 5y = t² + e²¯
into a system of first order differential equations in the form of
x'
Ax + ģ(t)
What are , A, and ģ(t)?
=
x(t)
x (t)
x (t)
x (t)
=
=
=
=
x₁ (t)
x₂ (t)
x3 (t).
x₁ (t)
x₂ (t)
x3 (t).
[T₁ (t)]
x₂ (t)
x3 (t).
X1
x₁ (t)
=
=
=
Y
Y
D
C
Y
x₂ (t) -
=
x3 (t).
Y
y'
2
"
A =
A
-
A =
cos t
A =
0
5
1
0
5
1 0
0
1
-2
-3
0 1 0
EH
-5
2
3
0
0
1
1
0
1
-2 -3
-3
1
0
0
1
-2 5
"
0 0 1 g(t)
2
2
g(t)
"
g(t)
=
g(t) =
=
e
-4t
0
0
+e-4t cos(t).
+ e
t²
0
0
-4t
cos(t)
cos(t).
0
0
t² + e-4t cos(t).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52872cac-4b45-467b-aca1-adaa6c0e02cd%2Ff6c6ed81-fb86-4b62-96d9-9742db0905a8%2Fmmu7ov_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Transfer the following differential equation:
- 4t
y" + 3y" + 2y' — 5y = t² + e²¯
into a system of first order differential equations in the form of
x'
Ax + ģ(t)
What are , A, and ģ(t)?
=
x(t)
x (t)
x (t)
x (t)
=
=
=
=
x₁ (t)
x₂ (t)
x3 (t).
x₁ (t)
x₂ (t)
x3 (t).
[T₁ (t)]
x₂ (t)
x3 (t).
X1
x₁ (t)
=
=
=
Y
Y
D
C
Y
x₂ (t) -
=
x3 (t).
Y
y'
2
"
A =
A
-
A =
cos t
A =
0
5
1
0
5
1 0
0
1
-2
-3
0 1 0
EH
-5
2
3
0
0
1
1
0
1
-2 -3
-3
1
0
0
1
-2 5
"
0 0 1 g(t)
2
2
g(t)
"
g(t)
=
g(t) =
=
e
-4t
0
0
+e-4t cos(t).
+ e
t²
0
0
-4t
cos(t)
cos(t).
0
0
t² + e-4t cos(t).
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