Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Related questions
Question
![**Solving Third-Order Initial Value Problems Using Laplace Transforms**
On this page, we will explore the process of solving a third-order initial value problem using Laplace transforms. Here is the problem statement:
\[ y''' + 7y'' + 7y' - 15y = -75, \]
with the initial conditions:
\[ y(0) = 8, \quad y'(0) = -9, \quad y''(0) = 75. \]
To assist you in solving this type of problem, we provide two essential resources:
1. [Table of Laplace Transforms](#)
2. [Table of Properties of Laplace Transforms](#)
Below, you can type your solution for \( y(t) \):
\[ y(t) = \boxed{\hspace{5cm}} \]
(Type an exact answer in terms of \( e \).)
**How to approach this problem:**
1. Start by taking the Laplace transform of each term in the differential equation.
2. Use the initial conditions to substitute into the transformed equation.
3. Solve the resulting algebraic equation for \( Y(s) \).
4. Apply the inverse Laplace transform to find \( y(t) \).
By following these steps, you can systematically solve third-order initial value problems involving differential equations. Remember to make use of the tables provided to assist with the transformations.
For further details and examples, click the links above to view the tables of Laplace transforms and their properties. These resources provide comprehensive information on how different functions and their derivatives transform under the Laplace operation.](https://content.bartleby.com/qna-images/question/45088ba1-a1a3-4a96-b462-54f2c0a5a29e/7f3cc8e4-a497-41b7-ab4d-a37765372323/yenl3lc_processed.jpeg)
Transcribed Image Text:**Solving Third-Order Initial Value Problems Using Laplace Transforms**
On this page, we will explore the process of solving a third-order initial value problem using Laplace transforms. Here is the problem statement:
\[ y''' + 7y'' + 7y' - 15y = -75, \]
with the initial conditions:
\[ y(0) = 8, \quad y'(0) = -9, \quad y''(0) = 75. \]
To assist you in solving this type of problem, we provide two essential resources:
1. [Table of Laplace Transforms](#)
2. [Table of Properties of Laplace Transforms](#)
Below, you can type your solution for \( y(t) \):
\[ y(t) = \boxed{\hspace{5cm}} \]
(Type an exact answer in terms of \( e \).)
**How to approach this problem:**
1. Start by taking the Laplace transform of each term in the differential equation.
2. Use the initial conditions to substitute into the transformed equation.
3. Solve the resulting algebraic equation for \( Y(s) \).
4. Apply the inverse Laplace transform to find \( y(t) \).
By following these steps, you can systematically solve third-order initial value problems involving differential equations. Remember to make use of the tables provided to assist with the transformations.
For further details and examples, click the links above to view the tables of Laplace transforms and their properties. These resources provide comprehensive information on how different functions and their derivatives transform under the Laplace operation.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 4 steps with 4 images
Knowledge Booster
Similar questions
- can you please show a clear working out on paperarrow_forwardSolve (i) (ii) (iii) (iv) and (v)arrow_forwardUse the formula {tf(t))} (s) = (-1)^({f}(s)) to help determine the following the expressions. dn ds" (a) {t cos bt} (b) {t² cos bt} Click here to view the table of Laplace transforms. (a) At cos bt}(s) =arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY 
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
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,