1. Consier the following 4th-order linear differential equations d4x + 10- dt3 d²x dx + 50 dt + 35 + 24x = 0 (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 = 1, dt d²x (0) = 0.5, d³x (0) = -0.3. x(0) = -1. (2) dt2 dt3
1. Consier the following 4th-order linear differential equations d4x + 10- dt3 d²x dx + 50 dt + 35 + 24x = 0 (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 = 1, dt d²x (0) = 0.5, d³x (0) = -0.3. x(0) = -1. (2) dt2 dt3
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
Concept explainers
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
PART A
![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%2F9429cf5a-f491-42f7-8bce-f26274f8d7e9%2Frhrvd_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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
