y" + 2y'- 3y = 2t² - 10cos(2t) + 3sin(4t) -e³t where y(0) = 2 and y'(0) = -4
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
pls give me the complete solution to this. 2nd pic is the answer.

Transcribed Image Text:1. Solve the following differential equation using Laplace method with respect to the given initial
conditions:
y" + 2y' - 3y = 2t² - 10cos(2t) + 3sin (4t) -e³t where y(0) = 2 and y'(0) = -4

Transcribed Image Text:1.
Input interpretation:
solve
Result:
y(t) =
==
8
13
y" (t) + 2 y' (t)-3 y(t) = 2t² - 10 cos(2 t) + 3 sin(4 t) - e³t
3t
y(0) = 2
y'(0) = -4
2t²
3
sin(2 t)
8t
+
57
425
-3t
56051 e
70 200
sin(4 t) +
+
14
13
177 et
136
cos(2 t)
3t
12
24
425
cos(4 t) -
28
27
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 4 steps with 4 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,

