or (s- hên using Appendix A, entries 17 and 9 with a = 4 and t replacing x, we obtain 8. x(1) = L"{X(s)}=L "' +16) 2 s +16 128 s +16 (s + 16) %3D 16 (sin 41 - 41 cos 41) 16 Compare with the results of Problem 14.10. Supplementary Problems Use Laplace transforms to solve the following problems. 24.17. y+2y = 0; y(0) = 1 24.18. y +2y =2; y(0) = 1 %3D %3D 24.19. y+ 2y= e*; y(0) = 1 24.20. y + 2y= 0; y(1) = 1 24.21. y+5y= 0; y(1) = 0 24.22. y - 5y=eS, y(0) = 2 %3D 24.23. y+y= xe*; y(0) =-2 24.24. y+y= sin x %3D %3D 24.25. y +20y = 6 sin 2x; y(0) = 6 24.26. y" - y= 0; y(0) = 1, y'(0) %3D %3D %3D %3D 24.27. y"-y= sin x; y(0) = 0, y'(0) = 1 24.28. y" -y= e*; y(0) = 1, y'(C %3D 24.29.) y" + 2y' – 3y = sin 2x; y(0) =y'(0) = 0 24.30. y" +y= sin x; y(0) = 0, %3D 24.31.) y" + y' + y= 0; y(0) = 4, y'(0) = -3 24.32. y" + 2y' + 5y= 3e2"; y 24.33. y" + 5y - 3y = u(x – 4); y(0) = 0, y'(0) = 0 24.34. y"+y= 0; y(7) = 0, y' 24.35.) y" - y = 5; y(0) = 0, y'(0) = 0, y"(0) = 0 24.36. y(4) – y = 0; y(0) = 1, %3D d’y 24.37. ) d - 34Y +3 - y = x°e*;y(0) = 1, y'(0) = 2, y"(0) = 3 dx³ .2 dx² dx dN 0.085N =0; N(0) = 5000 dt 24.38. 24.39. dt dl - 3T: T(0) =100 dT + 3T = 90; T(0) =100 dt dv + 2v = 32 dt 24.40. 24.41. dq 24.42. +q = 4cos 2t; q(0) =0 dt 24.43. +9x+14x=0; 24.44. *+4x +4x =0; x(0) =2, ¿(0) =-2 d²x dx 24.45. +8 +25.x di² dt
or (s- hên using Appendix A, entries 17 and 9 with a = 4 and t replacing x, we obtain 8. x(1) = L"{X(s)}=L "' +16) 2 s +16 128 s +16 (s + 16) %3D 16 (sin 41 - 41 cos 41) 16 Compare with the results of Problem 14.10. Supplementary Problems Use Laplace transforms to solve the following problems. 24.17. y+2y = 0; y(0) = 1 24.18. y +2y =2; y(0) = 1 %3D %3D 24.19. y+ 2y= e*; y(0) = 1 24.20. y + 2y= 0; y(1) = 1 24.21. y+5y= 0; y(1) = 0 24.22. y - 5y=eS, y(0) = 2 %3D 24.23. y+y= xe*; y(0) =-2 24.24. y+y= sin x %3D %3D 24.25. y +20y = 6 sin 2x; y(0) = 6 24.26. y" - y= 0; y(0) = 1, y'(0) %3D %3D %3D %3D 24.27. y"-y= sin x; y(0) = 0, y'(0) = 1 24.28. y" -y= e*; y(0) = 1, y'(C %3D 24.29.) y" + 2y' – 3y = sin 2x; y(0) =y'(0) = 0 24.30. y" +y= sin x; y(0) = 0, %3D 24.31.) y" + y' + y= 0; y(0) = 4, y'(0) = -3 24.32. y" + 2y' + 5y= 3e2"; y 24.33. y" + 5y - 3y = u(x – 4); y(0) = 0, y'(0) = 0 24.34. y"+y= 0; y(7) = 0, y' 24.35.) y" - y = 5; y(0) = 0, y'(0) = 0, y"(0) = 0 24.36. y(4) – y = 0; y(0) = 1, %3D d’y 24.37. ) d - 34Y +3 - y = x°e*;y(0) = 1, y'(0) = 2, y"(0) = 3 dx³ .2 dx² dx dN 0.085N =0; N(0) = 5000 dt 24.38. 24.39. dt dl - 3T: T(0) =100 dT + 3T = 90; T(0) =100 dt dv + 2v = 32 dt 24.40. 24.41. dq 24.42. +q = 4cos 2t; q(0) =0 dt 24.43. +9x+14x=0; 24.44. *+4x +4x =0; x(0) =2, ¿(0) =-2 d²x dx 24.45. +8 +25.x di² dt
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
No.24.29 differential equations
Transcribed Image Text:or
(s-
hên using Appendix A, entries 17 and 9 with a = 4 and t replacing x, we obtain
8.
x(1) = L"{X(s)}=L
"'
+16) 2
s +16
128
s +16
(s
+ 16)
%3D
16
(sin 41 - 41 cos 41)
16
Compare with the results of Problem 14.10.
Supplementary Problems
Use Laplace transforms to solve the following problems.
24.17. y+2y = 0; y(0) = 1
24.18. y +2y =2; y(0) = 1
%3D
%3D
24.19. y+ 2y= e*; y(0) = 1
24.20. y + 2y= 0; y(1) = 1
24.21. y+5y= 0; y(1) = 0
24.22. y - 5y=eS, y(0) = 2
%3D
24.23. y+y= xe*; y(0) =-2
24.24. y+y= sin x
%3D
%3D
24.25. y +20y = 6 sin 2x; y(0) = 6
24.26. y" - y= 0; y(0) = 1, y'(0)
%3D
%3D
%3D
%3D
24.27. y"-y= sin x; y(0) = 0, y'(0) = 1
24.28. y" -y= e*; y(0) = 1, y'(C
%3D
24.29.) y" + 2y' – 3y = sin 2x; y(0) =y'(0) = 0
24.30. y" +y= sin x; y(0) = 0,
%3D
24.31.) y" + y' + y= 0; y(0) = 4, y'(0) = -3
24.32. y" + 2y' + 5y= 3e2"; y
24.33. y" + 5y - 3y = u(x – 4); y(0) = 0, y'(0) = 0
24.34. y"+y= 0; y(7) = 0, y'
24.35.) y" - y = 5; y(0) = 0, y'(0) = 0, y"(0) = 0
24.36. y(4) – y = 0; y(0) = 1,
%3D
d’y
24.37. ) d - 34Y +3 - y = x°e*;y(0) = 1, y'(0) = 2, y"(0) = 3
dx³
.2
dx²
dx
dN
0.085N =0; N(0) = 5000
dt
24.38.
24.39.
dt
dl - 3T: T(0) =100
dT
+ 3T = 90; T(0) =100
dt
dv
+ 2v = 32
dt
24.40.
24.41.
dq
24.42.
+q = 4cos 2t; q(0) =0
dt
24.43. +9x+14x=0;
24.44. *+4x +4x =0; x(0) =2, ¿(0) =-2
d²x
dx
24.45.
+8 +25.x
di²
dt
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