Differential Equations and Linear Algebra, 4th Edition

Section 10.1

1. 1. $1/s^2,s>0$

2. 2. $2/s^3,s>0$

3. 3. $e/\left(s-3\right),s>3$

4. 4. $s/(s^2+1),s>0$

5. 5. $1/(s^2-1),s>1$

6. 6. $\frac{1}{2}[1/s-s/(s^2+4)],s>0$

7. 7. $(1-e^{-s})/s,s>0$

8. 8. $\left(e^{-s}-e^{-2s}\right)/s,s>0$

9. 9. $(1-e^{-s}-s{e}^{-s})/s^2,s>0$

10. 10. $(s-1+e^{-s})/s^2,s>0$

11. 11. $\frac{1}{2}\sqrt{\pi }{s}^{-3/2}+3s^{-2},s>0$

12. 12. $(45\pi -192s^{3/2})/(8s^{7/2}),s>0$

13. 13. $s^{-2}-2{(s-3)}^{-1},s>3$

14. 14. $3\sqrt{\pi }/(4s^{5/2})+1/(s+10),s>0$

15. 15. $s^{-1}+s{\left(s^2-25\right)}^{-1},s>5$

16. 16. $(s+2)/(s^2+4),s>0$

17. 17. ${\cos }^{2}2t=\frac{1}{2}(1+\cos 4t)$; $\frac{1}{2}[s^{-1}+s/(s^2+16)],s>0$

18. 18. $3/(s^2+36),s>0$

19. 19. $s^{-1}+3s^{-2}+6s^{-3}+6s^{-4},s>0$

20. 20. $1/{\left(s-1\right)}^2,s>1$

21. 21. $(s^2-4)/{(s^2+4)}^2,s>0$

22. 22. $\frac{1}{2}\left[s/\left(s^2-36\right)-s^{-1}\right]$

23. 23. $\frac{1}{2}{t}^3$

24. 24. $2\sqrt{t/\pi }$

25. 25. $1-\frac{8}{3}{t}^{3/2}{\pi }^{-1/2}$

26. 26. $e^{-5t}$

27. 27. $3e^{4t}$

28. 28. $3\cos 2t+\frac{1}{2}\sin 2t$

29. 29. $\frac{5}{3}\sin 3t-3\cos 3t$

30. 30. $-\cosh 2t-\frac{9}{2}\sinh 2t$

31. 31. $\frac{3}{5}\sinh 5t-10\cosh 5t$

32. 32. $2u(t-3)$

33. 37. $f(t)=1-u(t-a)$. Your figure should indicate that the graph of f contains the ...