1550078481-Ordinary_Differential_Equations__Roberts_

(jair2018) #1
Answers to Selected Exercises 561


  1. b. (i)


_ -2x -.322888 -4x 1.73580 -x -. 170219
(

.161444J ( -.433951J ( .170219J

u - cie - .16 1444 +c^2 e .433951 +c^3 e .170219

.322888 -1.73580 -.170219

(


  • .163779J






-5x .8 18897
C^4 e -.163779
.818897

(

-2x .00 .16J -2x. (-.32.8 0 J


u = c^1 [e cosx -.l 6 - e smx.


32
]
.00 -.80


  1. b. (ii)


(

+c2[e -2x smx. __ .16.^00 J -2x ( -.32.8 0 J
16

+e cosx _

32

]
.00 -.80

(

x -.307729 .307729J -3x ( -.3590351.07711 J
+ c^3 e- .307729 + c^4 e -.359035
-.307729 1.07711


  1. b. (iii)


+ c3[(e^1 x cosc5x)v3 - (e^1 x sinc5x)v4] + c4[(e^1 x sinc5x)v3 + (e^1 x cosc5x)v 4 ]

where a= -1, {3 = 1.73205, 'Y = -1, c5 = 1, and


(

.360288J
.000000

Vl = -.360288 '

.000000
(

-.208013J
.832050

V^2 = .208013 '

-.832050

(

.300463J
.0 00000
v^3 = .300463 ' and
.000000
(

-.300463J
.600925

V^4 = - .3 00463

.600925
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