Page 361 - Schaum's Outline of Differential Equations

344 ANSWERS TO SUPPLEMENTARY PROBLEMS

10
25
10
7.72. (a) q = 2 + 3e- '; (b) I = -30e- ' 7.73. (a) q=We- '; (b) I = -25e~ 2 5(

25t
7.77. (a) I=We- ; (b)I,= We- 25t

2
7.82. xy = k 7.83. y = -2x + k
2
2
7.85. x + y = kx

CHAPTER 8

8.33. (e), (g), (j), and (K) are nonlinear; all the rest are linear. Note that (/) has the form y' — (2 + x)y = 0.

x
8.34. (a), (c), and (/) are homogeneous. Note that (/) has the form y" = -e .
8.35. (b), (c), and (/) have constant coefficients. 8.36. W= 0

2
4
8.37. W= —x ; the set is linearly independent. 8.38. W= —x ; the set is linearly independent.
3
8.39. W=-2x ; the set is linearly independent 8.40. W= -Wx; the set is linearly independent.
8.41. W=0 8.42. W=-4; the set is linearly independent.

5x
8.43. W= e ; the set is linearly independent. 8.44. W=0
8.45. W=0 8.46. W=0
2x
6
8.47. W= 2x ; the set is linearly independent. 8.48. W= 6e ; the set is linearly independent.
8.49. W=0 8.50. [4]3x + [-3]4x = 0

2
2
2
2x
8.51. [1]^ +[1](-^ ) = 0 8.52. [5](3e ) + [-3](5e *) = 0
8.53. [-2]x+[7](l) + [l](2x-7) = 0 8.54. [3](x + 1) + [-2](x 2 + x)
2
+ [l](2x -x-3) = 0