Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the following initial value problem: Edit y" + 8y' + 15y = d(t – 5) + u10(t); y(0) = 0, y(0) 4 a) Find the solution y(t). y(t) 8. -3t - e 1 -3(t-5) e 1 -5(t-5) u(t) X 1 e5(t–10) 10 1 -3(t-10) e ua(t) 6. 15 where c= and d =10

Consider the following initial value problem: Edit y" + 8y' + 15y = d(t – 5) + u10(t); y(0) = 0, y(0) 4 a) Find the solution y(t). y(t) 8. -3t - e 1 -3(t-5) e 1 -5(t-5) u(t) X 1 e5(t–10) 10 1 -3(t-10) e ua(t) 6. 15 where c= and d =10

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
**Initial Value Problem and Its Solution** Consider the following initial value problem: \[ y'' + 8y' + 15y = \delta(t - 5) + u_{10}(t); \quad y(0) = 0, \quad y'(0) = \frac{1}{4} \] **a) Find the solution \( y(t) \).** The solution to the problem is given by: \[ y(t) = \frac{1}{8} \left( e^{-3t} - e^{-5t} \right) \] \[ + \left( \frac{1}{2} \left( e^{-3(t-5)} - \frac{1}{2} e^{-5(t-5)} \right) \right) u_c(t) \] \[ + \left( -\frac{1}{6} e^{-3(t-10)} + \frac{1}{10} e^{-5(t-10)} + \frac{1}{15} \right) u_d(t) \] where \( c = 5 \) and \( d = 10 \).
Transcribed Image Text:**Initial Value Problem and Its Solution** Consider the following initial value problem: \[ y'' + 8y' + 15y = \delta(t - 5) + u_{10}(t); \quad y(0) = 0, \quad y'(0) = \frac{1}{4} \] **a) Find the solution \( y(t) \).** The solution to the problem is given by: \[ y(t) = \frac{1}{8} \left( e^{-3t} - e^{-5t} \right) \] \[ + \left( \frac{1}{2} \left( e^{-3(t-5)} - \frac{1}{2} e^{-5(t-5)} \right) \right) u_c(t) \] \[ + \left( -\frac{1}{6} e^{-3(t-10)} + \frac{1}{10} e^{-5(t-10)} + \frac{1}{15} \right) u_d(t) \] where \( c = 5 \) and \( d = 10 \).
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS