96
LINEAR DIFFERENTIAL EQUATIONS
Answers to Supplementary Problems 3.49.
(a) (D2 + 4D + 5)y = e~x,
3.50.
(a) Both equal sin 2x - 8 cos 2x.
3.51.
(a) -2*2 - 8x + 21. -2a;2 - 6» + 22, (6) No
3.52.
(a) Sx2 + 2a;3ea: + Ba^e* + 2xex
3.56.
y
3.59.
(a) y
3.60.
(a) j/
(6) (2Z>« + 2D- l)y = x,
(6) Yes
3.55.
=
(c) y
3.61.
(a) y
(c) y (d) V
(•) y 3.62.
j/ = ct 4
3.63.
(a) j/ = (6) y =
3.64.
(o) y =
3.65.
y =
3.66.
(a) j/ =
C l -I
(6) V = (c) y = (<*) y =
3.67.
(a) (6) (c)
3.68.
(o) y = (6) y = (c) !/ =
3.70.
(a) y =
(d) V = (e) R = 3.71. 3.73.
(c) (xD + 2)y = 1
3.74.
Functions are linearly independent.
[CHAP. 3