Page 110 - Schaum's Outline of Differential Equations
P. 110
CHAP. 10] wth-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS 93
Supplementary Problems
In Problems 10.16 through 10.34, solve the given differential equations.
10.16. /" - 2y" -y' + 2y = 0 10.17. y'" -/'- y' + y = 0
10.18. y'" - 3y" + 3y'-y = 0 10.19. y'" ~ /' + / ~ y = 0
10.20. -y(4) + 2y" + y = Q 10.21. /4> ~y = 0
10.22. -y(4) + 2y'» -2y'-y = Q 10.,23. -y(4) -4y" + 16/ + 32y = 0
10.24. yW + 5y'" = 0 10.,25. /4> + 2y"' + 3y" + 2y' + y = 0
(6)
4)
10.26. ;y - 5/ + 16/" + 36/' - 16/ - 32;y = 0
(4)
10.31. q + q"-2q = 0
w
10.32. q - 3q" + 2q = 0 10.33. N"'- 12N"- 28N + 480N= 0
In Problems 10.35 through 10.41, a complete set of roots is given for the characteristic equation of an wth-order near homoge-
neous differential equation in y(x) with real numbers as coefficients. Determine the general solution of the differential equation.
10.35. 2, 8,-14
10.39. 5, 5, 5,-5,-5
10.42. Determine the differential equation associated with the roots given in Problem 10.35.
10.43. Determine the differential equation associated with the roots given in Problem 10.36.
10.44. Determine the differential equation associated with the roots given in Problem 10.37.
10.45. Determine the differential equation associated with the roots given in Problem 10.38.
10.46. Determine the differential equation associated with the roots given in Problem 10.39.
10.47. Find the general solution to a fourth-order linear homogeneous differential equation for y(x) with real numbers as
3
coefficients if one solution is known to be x e~ . x
10.48. Find the general solution to a fourth-order linear homogeneous differential equation for y(x) with real numbers as
coefficients if two solutions are cos 4x and sin 3x.
10.49. Find the general solution to a fourth-order linear homogeneous differential equation for y(x) with real numbers as
coefficients if one solution is x cos 4x.
10.50. Find the general solution to a fourth-order linear homogeneous differential equation for y(x) with real numbers as
2x
5x
coefficients if two solutions are xe and xe .
