In each of Problems 17 through 19, find the Laplace transform Y(s) = Lly) 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. 1, 0≤1
In each of Problems 17 through 19, find the Laplace transform Y(s) = Lly) 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. 1, 0≤1
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
17
Transcribed Image Text:e
10.
y"-2y' + 2y = 0;
y(0) = 0,
y'(0) = 1
1. y"-2y' +4y=0;
y(0) = 2,
y'(0) = 0
12. y" +2y + 5y = 0;
y(0) = 2,
y'(0) = -1
13. y(4) - 4y + 6y" - 4y + y = 0; y(0) = 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; y(0) = 1, y'(0) = 0
16. y"-2y' +2y=e¹; y(0) = 0, y'(0) = 1
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.
1,
0≤1<T,
_17. y" + 4y = {0, a ≤1 < 00:
0 ≤ t < 1,
18. y" +4y=
19.
{
1, 1≤1<∞0;
y"+y=2-1,
0,
0 ≤1 <1,
y(0) = 1, y'(0) = 0
y(0) = 0, y'(0) = 0
1≤t<2, y(0) = 0, y'(0) = 0
2 ≤ 1 <∞0;
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