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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 43RE
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2 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;
Transcribed Image Text:2 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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