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0 ≤t < 1, y"+y=<2-t, 1 ≤ t < 2, y(0) = 0, y'(0)=0 0, 2≤t < 8;

0 ≤t < 1, y"+y=<2-t, 1 ≤ t < 2, y(0) = 0, y'(0)=0 0, 2≤t < 8;

Advanced Engineering Mathematics
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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rm istan not 17. y" + 4y = 18. y" +4y= 10. y"-2y' + 2y = 0; y(0) = 0, 11. y"-2y' + 4y = 0; y(0) = 2, y(0) = 2, 12. y" +2y' + 5y = 0; 13. (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 D (138) ollib or suaminigol al 15. y" +w²y = cos(2t), w² #4; y(0) = 1, 16. y"-2y' +2y=e¹; y(0) = 0, y'(0) = 11 wodd e 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 6.1.0 dono al lanan soalqal sd y'(0) = 0 y(0) = 1, ft, 1, 1≤t<∞0; {1 [1, 0≤t<,vito 10, π ≤ t < 00; 0≤t< 1, 19. y"+y=2-t, A 8; {(\)}2 y'(0) = 1d 1 amoldon y'(0) = 0 molanan sosiga. y'(0) = -1 15.1 bre 11 S.1.0 monood T y'(0) = 0 diw 2: 0, 2≤1<∞0; y(0) = 0, y'(0) = 0 0 ≤ t < 1, 1≤t<2, y(0) = 0, y'(0) = 0
Transcribed Image Text:rm istan not 17. y" + 4y = 18. y" +4y= 10. y"-2y' + 2y = 0; y(0) = 0, 11. y"-2y' + 4y = 0; y(0) = 2, y(0) = 2, 12. y" +2y' + 5y = 0; 13. (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 D (138) ollib or suaminigol al 15. y" +w²y = cos(2t), w² #4; y(0) = 1, 16. y"-2y' +2y=e¹; y(0) = 0, y'(0) = 11 wodd e 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 6.1.0 dono al lanan soalqal sd y'(0) = 0 y(0) = 1, ft, 1, 1≤t<∞0; {1 [1, 0≤t<,vito 10, π ≤ t < 00; 0≤t< 1, 19. y"+y=2-t, A 8; {(\)}2 y'(0) = 1d 1 amoldon y'(0) = 0 molanan sosiga. y'(0) = -1 15.1 bre 11 S.1.0 monood T y'(0) = 0 diw 2: 0, 2≤1<∞0; y(0) = 0, y'(0) = 0 0 ≤ t < 1, 1≤t<2, y(0) = 0, y'(0) = 0
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