1. Consier the following 4th-order linear differential equations d²x + 10- dt3 dx + 24x = 0 dt + 35 + 50 (1) dt4 dt2 (a) and eigenvectors for the corresponding system A matrix. Convert this into a first order linear system and use Python to find the eigenvalues (b) Using part a) find the general solution of the system. (c) Using part a) and b) find the solution of the ODE for initial conditions dx x(0) : (0) () = = 0.5, (0) = -0.3. dt3 (2) = 1, = -1, dt dt2 You must plot x(t), (t) over the time interval [0, 10]. Take AT = 0.01. Note: You can use Python for any linear algebraic computation required such as computing the determinant. inversion of matrix, trace of matrix etc. Do not use the forward Euler algorithm or odeint to find the solution. :
1. Consier the following 4th-order linear differential equations d²x + 10- dt3 dx + 24x = 0 dt + 35 + 50 (1) dt4 dt2 (a) and eigenvectors for the corresponding system A matrix. Convert this into a first order linear system and use Python to find the eigenvalues (b) Using part a) find the general solution of the system. (c) Using part a) and b) find the solution of the ODE for initial conditions dx x(0) : (0) () = = 0.5, (0) = -0.3. dt3 (2) = 1, = -1, dt dt2 You must plot x(t), (t) over the time interval [0, 10]. Take AT = 0.01. Note: You can use Python for any linear algebraic computation required such as computing the determinant. inversion of matrix, trace of matrix etc. Do not use the forward Euler algorithm or odeint to find the solution. :
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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Question
PART C
![1. Consier the following 4th-order linear differential equations
dx
+ 10-
dt3
+ 35
dt?
+ 50
(1)
+ 24x = 0
dt4
dt
(a)
and eigenvectors for the corresponding system A matrix.
Convert this into a first order linear system and use Python to find the eigenvalues
(b)
Using part a) find the general solution of the system.
(c)
Using part a) and b) find the solution of the ODE for initial conditions
dx
x(0) = 1,
(0):
-1,
dt2
(0) = 0.5,
(0),
= -0.3.
(2)
dt
dt3
dx
You must plot x(t), (t) over the time interval [0, 10]. Take AT = 0.01.
Note: You can use Python for any linear algebraic computation required such as computing
the determinant. inversion of matrix, trace of matrix etc.
Do not use the forward Euler algorithm or odeint to find the solution. :
, dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe25f92a2-1c4d-41a3-af19-0cdf00d27604%2Fb7f7816c-5a26-48f6-8d51-c261ec6845ec%2F6st9pt_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consier the following 4th-order linear differential equations
dx
+ 10-
dt3
+ 35
dt?
+ 50
(1)
+ 24x = 0
dt4
dt
(a)
and eigenvectors for the corresponding system A matrix.
Convert this into a first order linear system and use Python to find the eigenvalues
(b)
Using part a) find the general solution of the system.
(c)
Using part a) and b) find the solution of the ODE for initial conditions
dx
x(0) = 1,
(0):
-1,
dt2
(0) = 0.5,
(0),
= -0.3.
(2)
dt
dt3
dx
You must plot x(t), (t) over the time interval [0, 10]. Take AT = 0.01.
Note: You can use Python for any linear algebraic computation required such as computing
the determinant. inversion of matrix, trace of matrix etc.
Do not use the forward Euler algorithm or odeint to find the solution. :
, dt
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