Find a solution to the system [*] -3 1 1 -5 [] [] by solving the IVP with initial condition x (t) B exp( t) + 18 = y(0) || 8 3 t exp ☐t)
Find a solution to the system [*] -3 1 1 -5 [] [] by solving the IVP with initial condition x (t) B exp( t) + 18 = y(0) || 8 3 t exp ☐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
![Find a solution to the system
[*]
-3 1
1 -5
[] []
by solving the IVP with initial condition
x (t)
exp
t) +
18
=
3
[8] = [³]
y(0)
t exp
☐t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa86b2d75-dc89-44ee-816d-e64b811f53cb%2F32f40642-0843-4dfa-8f98-9852e09b4fe0%2Fk39zujs_processed.png&w=3840&q=75)
Transcribed Image Text:Find a solution to the system
[*]
-3 1
1 -5
[] []
by solving the IVP with initial condition
x (t)
exp
t) +
18
=
3
[8] = [³]
y(0)
t exp
☐t)
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Follow-up Questions
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Follow-up Question
![Find a solution to the system
1
[]=[ +][0]
3
- 1
¯x(0)
by solving the IVP with initial condition
[20] - [3³]
=
y(0)
3
x(t)
8
B
exp(-4t) +
t exp(-4✓t)
-4
Part 2 of 3
Now take the derivative of the above solution and subtract – 47(t) to obtain a second solution to the
differential equation.
x'(t) + 4x(t) =
13
exp(-4t)
४
=](https://content.bartleby.com/qna-images/question/a86b2d75-dc89-44ee-816d-e64b811f53cb/1336a491-538d-48bc-86d8-5e8a5a05b781/r0k2bda_processed.png)
Transcribed Image Text:Find a solution to the system
1
[]=[ +][0]
3
- 1
¯x(0)
by solving the IVP with initial condition
[20] - [3³]
=
y(0)
3
x(t)
8
B
exp(-4t) +
t exp(-4✓t)
-4
Part 2 of 3
Now take the derivative of the above solution and subtract – 47(t) to obtain a second solution to the
differential equation.
x'(t) + 4x(t) =
13
exp(-4t)
४
=
Solution
by Bartleby ExpertFollow-up Question
![Find a solution to the system
- 3
1
[]
s] [*]
- 1
by solving the IVP with initial condition
4
x(t)
=
=
+
¯x (0)
.y(0)
exp(-4✔ o t) +
3
=
1
[8]
t exp(-4✓t)](https://content.bartleby.com/qna-images/question/a86b2d75-dc89-44ee-816d-e64b811f53cb/4581d010-26f9-47fd-980b-83ef37a524d1/f4olgpm_processed.png)
Transcribed Image Text:Find a solution to the system
- 3
1
[]
s] [*]
- 1
by solving the IVP with initial condition
4
x(t)
=
=
+
¯x (0)
.y(0)
exp(-4✔ o t) +
3
=
1
[8]
t exp(-4✓t)
Solution
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