a) Construct a 2nd order differential equation with constant coefficients whose characteristic equation has unique roots neither of which are 0. Taking as the initial values y(0) = a, and y'(0) = b, (a,b pair assigned) solve the homogeneous equation (set equal to 0) by Laplace Transform.
a) Construct a 2nd order differential equation with constant coefficients whose characteristic equation has unique roots neither of which are 0. Taking as the initial values y(0) = a, and y'(0) = b, (a,b pair assigned) solve the homogeneous equation (set equal to 0) by Laplace Transform.
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
a=-2 and b=1
![a) Construct a 2nd order differential equation with constant coefficients whose characteristic equation
has unique roots neither of which are 0. Taking as the initial values y(0) = a, and y'(0) = b, (a, b
pair assigned) solve the homogeneous equation (set equal to 0) by Laplace Transform.
b) Using a) above, solve for the right hand side (bt+a)et with the initial values y(0) = b and y'(0) = 0
(b assigned) by Laplace Transform.
c) Construct a 2nd order differential equation with constant coefficients whose characteristic equation
has unique roots neither of which are 0. This DE must be different from a) above. Form the following
right-hand-side using your a, b pair :
g(t) = {
a
bt
g(t) =
0 ≤ t <3
t≥ 3
Solve this using Laplace Transform using the initial values y(0) = 1 and y'(0) = 0.
d) For the differential equation you constructed in c) above, form the following right-hand-side using
your a, b pair:
a
at² + b
bt + a
0 ≤t <2
2 <t
t> 4
Solve this using Laplace Transform using the initial values y(0)
= 1 and y'(0) =
= 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0436118d-47b7-4fa9-abd3-dac72bbeccd1%2Fcab8f57d-b9b3-4169-9b41-0e41c310114d%2F4oih42g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Construct a 2nd order differential equation with constant coefficients whose characteristic equation
has unique roots neither of which are 0. Taking as the initial values y(0) = a, and y'(0) = b, (a, b
pair assigned) solve the homogeneous equation (set equal to 0) by Laplace Transform.
b) Using a) above, solve for the right hand side (bt+a)et with the initial values y(0) = b and y'(0) = 0
(b assigned) by Laplace Transform.
c) Construct a 2nd order differential equation with constant coefficients whose characteristic equation
has unique roots neither of which are 0. This DE must be different from a) above. Form the following
right-hand-side using your a, b pair :
g(t) = {
a
bt
g(t) =
0 ≤ t <3
t≥ 3
Solve this using Laplace Transform using the initial values y(0) = 1 and y'(0) = 0.
d) For the differential equation you constructed in c) above, form the following right-hand-side using
your a, b pair:
a
at² + b
bt + a
0 ≤t <2
2 <t
t> 4
Solve this using Laplace Transform using the initial values y(0)
= 1 and y'(0) =
= 0.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)