L{y(t)} = (s/((s+36)(s^2+36)))+((8+7s)/(s^2+36)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = ((99/74)sin(6t))-((1/37)e^(-36t))+((260/37) cos(6t))
L{y(t)} = (s/((s+36)(s^2+36)))+((8+7s)/(s^2+36)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = ((99/74)sin(6t))-((1/37)e^(-36t))+((260/37) cos(6t))
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
Here is the problem. Why is my third answer wrong?
![**Results for this submission**
| Entered | Answer Preview | Result | Message |
|-----------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------|------------|----------------------------------------------------------|
| (s^2)*Y(s)-7*s-8+36*Y(s) | \( s^2Y(s) - 7s - 8 + 36Y(s) \) | correct | |
| s/[(s^2)+36] | \( \frac{s}{s^2 + 36} \) | correct | |
| (s/[(s+36)*[(s^2)+36]])+[(8+7*s)/[(s^2)+36]] | \( \frac{s}{(s + 36)(s^2 + 36)} + \frac{8 + 7s}{s^2 + 36} \) | correct | |
| (99/74)*sin(6*t)-(1/37)*[e^(-36*t)]+(260/37)*cos(6*t) | \( \frac{99}{74}\sin(6t) - \frac{1}{37}e^{-36t} + \frac{260}{37}\cos(6t) \) | incorrect | This answer is equivalent to the one you just submitted. |
**Explanation of Graphs or Diagrams:**
There are no graphs or diagrams present. The table shows the entered mathematical expressions, the expected answer previews, the results indicating whether each submission was correct or incorrect, and any messages related to the entries.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50676bcf-7237-4f00-9235-8bc1502a02cd%2F9db558b5-e496-4b49-b0d3-da44b32ff6ed%2Fso56pr7_processed.png&w=3840&q=75)
Transcribed Image Text:**Results for this submission**
| Entered | Answer Preview | Result | Message |
|-----------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------|------------|----------------------------------------------------------|
| (s^2)*Y(s)-7*s-8+36*Y(s) | \( s^2Y(s) - 7s - 8 + 36Y(s) \) | correct | |
| s/[(s^2)+36] | \( \frac{s}{s^2 + 36} \) | correct | |
| (s/[(s+36)*[(s^2)+36]])+[(8+7*s)/[(s^2)+36]] | \( \frac{s}{(s + 36)(s^2 + 36)} + \frac{8 + 7s}{s^2 + 36} \) | correct | |
| (99/74)*sin(6*t)-(1/37)*[e^(-36*t)]+(260/37)*cos(6*t) | \( \frac{99}{74}\sin(6t) - \frac{1}{37}e^{-36t} + \frac{260}{37}\cos(6t) \) | incorrect | This answer is equivalent to the one you just submitted. |
**Explanation of Graphs or Diagrams:**
There are no graphs or diagrams present. The table shows the entered mathematical expressions, the expected answer previews, the results indicating whether each submission was correct or incorrect, and any messages related to the entries.
![Consider the initial value problem
\[
y'' + 36y = \cos(6t), \quad y(0) = 7, \quad y'(0) = 8.
\]
a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of \(y(t)\) by \(Y(s)\). Do not move any terms from one side of the equation to the other (until you get to part (b) below).
\[
(s^2Y(s)) - 7s - 8 + 36Y(s) = \frac{s}{s^2 + 36}
\]
b. Solve your equation for \(Y(s)\).
\[
Y(s) = \mathcal{L}\{y(t)\} = \left(\frac{s}{((s+36)(s^2+36))}\right) + \left(\frac{(8+7s)}{(s^2+36)}\right)
\]
c. Take the inverse Laplace transform of both sides of the previous equation to solve for \(y(t)\).
\[
y(t) = \left(\frac{99}{74}\sin(6t)\right) - \left(\frac{1}{37}e^{-36t}\right) + \left(\frac{260}{37}\cos(6t)\right)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50676bcf-7237-4f00-9235-8bc1502a02cd%2F9db558b5-e496-4b49-b0d3-da44b32ff6ed%2Fnd7qf7v_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem
\[
y'' + 36y = \cos(6t), \quad y(0) = 7, \quad y'(0) = 8.
\]
a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of \(y(t)\) by \(Y(s)\). Do not move any terms from one side of the equation to the other (until you get to part (b) below).
\[
(s^2Y(s)) - 7s - 8 + 36Y(s) = \frac{s}{s^2 + 36}
\]
b. Solve your equation for \(Y(s)\).
\[
Y(s) = \mathcal{L}\{y(t)\} = \left(\frac{s}{((s+36)(s^2+36))}\right) + \left(\frac{(8+7s)}{(s^2+36)}\right)
\]
c. Take the inverse Laplace transform of both sides of the previous equation to solve for \(y(t)\).
\[
y(t) = \left(\frac{99}{74}\sin(6t)\right) - \left(\frac{1}{37}e^{-36t}\right) + \left(\frac{260}{37}\cos(6t)\right)
\]
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 2 steps with 2 images
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,
