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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17 please
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10. y"-2y' + 2y = 0;
y(0) = 0,
11.
y" - 2y + 4y = 0;
y(0) = 2,
12. y" +2y + 5y = 0;
y(0) = 2,
13. y(4) - 4y +6y" - 4y' + y = 0; y(0) = 0,
y'(0) = 1, y"(0) = 0, y""(0) = 1
14. (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) =
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.
y(0) = 1, y'(0) = 0
17. y" + 4y =
1,
0≤1<T,
0, π ≤1 < 00;
0 ≤ t < 1,
1≤t<∞0;
{1
18. y" + 4y = { 1
1,
y'(0) = 1
y'(0) = 0
y'(0) = -1
1₂
19. y"+y=2-1,
0,
y(0) = 0, y'(0) = 0
0 ≤ t < 1,
1≤1<2, y(0) = 0, y'(0) = 0
2 ≤ 1 <∞0;
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