In each of Problems 8 through 16, use the Laplace transform tc the given initial value problem. 6y=0; y(0) = 1, y'(0) = -1 8. y" - y - 9. y" + 3y + 2y = 0; y(0) = 1, y'(0) = 0
In each of Problems 8 through 16, use the Laplace transform tc the given initial value problem. 6y=0; y(0) = 1, y'(0) = -1 8. y" - y - 9. y" + 3y + 2y = 0; y(0) = 1, y'(0) = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
15 please
Transcribed Image Text:is of
nding physical problem
In the problem lists following this and other sections in this chapter are numerous initial-
value problems for second-order linear differential equations with constant coefficients. Many
can be interpreted as models of particular physical systems, but usually we do not point this
out explicitly.
Problems
In each of Problems 1 through 7, find the inverse Laplace transform
of the given function.
3
1. F(s):
Lan (1) 4
2. F(s) =
=
3. F(s) =
4. F(s) =
5. F(s) =
·5² +4
6. F(s) =
(S-1)³
2
s² + 3s - 4
2s +2
s² +2s +5
2s 3
5²-4
8s² - 4s + 12
s(s² + 4)
1-2s
1
bas (up t
mu vodsvloviconam
8. y" - y' -6y=0;
9. y" + 3y +2y=0;
7. F(s) =
$²+4s +5
In each of Problems 8 through 16, use the Laplace transform to solve
the given initial value problem.
HUM
y(0) = 1, y'(0) = -1
y(0) = 1, y'(0) = 0
10.
y" - 2y' +2y=0;
y(0) = 0,
y(0) = 2,
11.
y" - 2y + 4y = 0;
12.
y" + 2y + 5y = 0;
y(0) = 2,
13.
y(4) - 4y"" + 6y" - 4y' + y = 0;
y'(0) = 1, y"(0) = 0, y""(0) = 1
14. y(4) - y = 0; y(0) = 1, y'(0) = 0, y" (0) = 1,
y" (0) = 0
15. y"+w²y = cos(21), w² #4;
16. y" - 2y + 2y = e'; y(0) = 0, y'(0) = 1
17. y" + 4y =
(A
18. y" + 4y =
In each of Problems 17 through 19, find the Laplace transform Y(s) =
L{y} of the solution of the given initial value problem. A method of
determining the inverse transform is developed in Section 6.3. You
may wish to refer to Problems 16 through 18 in Section 6.1.
y(0) = 1, y'(0) = 0
1, 0≤t<T,
0,
y'(0) = 1
y'(0) = 0
y'(0) = -1
y(0) = 0,
۔ ن
0 ≤t< 1,
1, 1≤1 < 00;
π ≤1<∞0;
I
19. y"+y=2-1,
0,
y(0) = 1, y'(0) = 0
y(0) = 0, y'(0) = 0
0 ≤t < 1,
1st <2, y(0) = 0, y'(0) = 0
2 ≤1 < 00;
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