Page 392 - Schaum's Outline of Differential Equations

ANSWERS TO SUPPLEMENTARY PROBLEMS 375

085
24.38. JV=5000e°- '
24.40. r=70e- ' + 30
3

2t
24.41. v = d ae- + 16 (d a = c a- 16)
24.44. x = 2(l + t)e- '
2

4(
n)
24.45. x = -2e- '- sm3t

CHAPTER 25

2x
25.7. u(x)=x 2 + x v(x)=x-l 25.8. u(x) = e + 2e- x v(x) = e + e~ x
2x
25.9. u(x) = 2e* + 6e~ x v(x) = e* + 2e~ x 25.10. y(x) = l z(x)=x

5x
x
25.11. y(x) = e* z(x) = e x 25.12. w(x) = e - e- + 1
x
Sx
y(x) = 2e + e- -l
x
25.13. w(x) = cos x + sin x 25.14. u(x) = -if + e- x v(x) = e - e~ x
y(x) = cos x - sin x z(x) = 1
2
2x
25.15. u(x) = e +l v(x) = 2s * - 1 25.16. w(x) = x 2 y(x) = x z(x) = 1
25.17. w(x) = sin x y(x) = — 1 + cos x
z(x) = sin x - cos x

CHAPTER 26

26.15. x = k 1 cos t + k 2 sin t 26.16. x = 0

2
26.17. x = -cos(t- 1) + t 26.18. y = k 3e-' + k 4e '

26.19. y = e-' + e 2t