1550078481-Ordinary_Differential_Equations__Roberts_

546 Ordinary Differential Equations

Chapter 3 APPLICATIONS OF THE INITIAL VALUE

PROBLEM: y' = f(x,y); y(c) = d

Exercises 3.1 Calculus Revisited

l. .8413004 3 .. 1393828

5. Does not exist. (Note that the integral is an improper integral.)


6. 1.118413
   . 15. .8818989

9 .. 1857833

17. 1.54787

11 .. 9096077

19. 8.933486

13. 1.352778
    21. 1.586823

23. a. 4.2356121f = 13.30657 b. 2.8788771f = 9.0442589

25. a. 4.5911691f = 14.42358 b. 12.001431f = 37.70360

27. a. Bx = 86.967951f = 273.2179 Vx = 4001f /3 ~ 418.879

b. Sy= 75 .083221f = 235.8809 Vy= 3207r/3 ~ 335.1032

29. a. Bx = 24.830541f = 78.00744 Vx = 12.588261f = 39.54720

· b. Sy = ll.9097921f = 37.415715 Vy= 6.2940441f = 19.77 332

31. a. Vx = .45614571f = 1.433024 b. Vy= .l 785857r = .5610416

33. a. Vx = 2.3552431f = 7.399214 b. Vy= .94729641f = 2.976019

35. A = l27r^3 ~ 372 .07532 s = 24 .439576


36. A= 18.84954 s = 16 39. A= 12.56623

41. A = 8 .3 37780 si = 2.682437 s 0 = 10.68242

45. A = 201f ~ 62.83185 s = 28 .36161

s = 99.95802

43. 
    

    78.53941

    
    


44. 
    

    A= 21f ~ 6.283186 s = 16 49. s = 39.47825

    
    

Exercises 3.2 Learning Theory Models

l. 15 .8 min., 41.6 min. Both values are larger than the values in example l.