1550078481-Ordinary_Differential_Equations__Roberts_

Answers to Selected Exercises 557

(

.5 + .5i)

V 3 = -.5_~ .5i

5. Al = 5, A2 = 3, A3 = 2, V 1 = ( ~--~:~~~

2

) , V2 = (-~:~~:~~) ,

.5 80015 -3. 08415

(

-4.47214)

V 3 = 4.47214

4.47214

7. 
   

   
   

   -1 = 0 , >- 2 = 64,
   (

   
   

   
   
   • .995495 )
     .0316030
     ,\^3 = O, ,\^4 = O, Vl =. .0474045 '
     .0 948091
   
   

   
   

   
   

(

-.-.329610 164805) (-.59694.923712 1) (-1.85119 -1.60790 )

V^2 = -.494415 ' V^3 = -.11 4431 ' V^4 = 1.08815

-.988829 -.228863 .176304

Exercises 8.3 Linear Systems with Constant Coefficients

7. y = c 1 (=:!~!~) e-x + c 2 (~:~) ex+ c 3 (~::~:) e^2 x

• .8 16497 1.73205 1.41421

(

- .894427) ( .745356) ( -.511827)

11. y = c 1 -.447214 e-^3 x +c2 -.745356 +c 3 .244087 e-^3 x

-.447214 .7 45356 .755913