.


:




:

































 

 

 

 





. :

b i , r . r - .

y 1, y 2,¼, yr. y 1 , ; y 2 , , .. , y 1, y 2,¼, yr, . y 1, y 2,¼, yr, , .

7

10-5 [0, 1] (0) = 0.

( ), . , .

k
  x ' = cos(at + x) + k (t x) 1.00 0.50
  -"- 1.25 0.75
  -"- 1.50 1.00
  -"- 1.75 1.25
  -"- 2.00 1.50
  x ' = 1 sin(at + x) + 1.00 - 0.3
  -"- 1.25 - 0.1
  -"- 1.50 0.1
  -"- 1.75 0.3
  -"- 2.00 0.5
  x ' = + k x 2 1.00 - 0.5
  -"- 1.25 - 0.3
  -"- 1.50 - 0.1
  -"- 1.75 0.1
  -"- 2.00 0.3
  x ' = 1 + (a t)sin(x) (k + t) x 0.50 1.00
  -"- 0.75 1.25
  -"- 1.00 1.50
  -"- 1.25 1.75
  -"- 1.50 2.00
  x ' = (a x 2)cos(t) + k x 0.6 0.2
  -"- 0.7 0.3
  -"- 0.8 0.4
  -"- 0.9 0.5
  -"- 1.0 0.6

 

a k
  x ' = 1 + a x sin(t) k x 2 0.2 1.00
  -"- 0.4 1.25
  -"- 0.6 1.50
  -"- 0.8 1.75
  -"- 1.0 2.00
  x ' = a e (a + t x) + k (t 2 + x) 0.2 0.3
  -"- 0.4 0.4
  -"- 0.6 0.5
  -"- 0.8 0.6
  -"- 1.0 0.7
  x ' = 0.1 0.1
  -"- 0.2 0.2
  -"- 0.3 0.3
  -"- 0.4 0.4
  -"- 0.5 0.5
  x ' = 0.2 ch(a t + x) + 0.3 1.00
  -"- 0.4 1.25
  -"- 0.5 1.50
  -"- 0.6 1.75
  -"- 0.7 2.00
  - 0.5 0.2
  -"- - 0.4 0.3
  -"- - 0.3 0.4
  -"- - 0.2 0.5
  -"- - 0.1 0.6

1. Maple :

h = 0.05 .

2. Mathcad .

"" ( ) . rkfixed ( - ) .

 

0 0

0.05000000000000 0.00084520959923

0.10000000000000 0.00343083039397

0.15000000000000 0.00783786372686

0.20000000000000 0.01415598922061

0.25000000000000 0.02248458081565

0.30000000000000 0.03293379527424

0.35000000000000 0.04562590720360

0.40000000000000 0.06069676562373

0.45000000000000 0.07829758606469

0.50000000000000 0.09859694045094

0.55000000000000 0.12178321860328

0.60000000000000 0.14806740950846

0.65000000000000 0.17768656848628

0.70000000000000 0.21090780566410

0.75000000000000 0.24803330959979

0.80000000000000 0.28940623751877

0.85000000000000 0.33541823340112

0.90000000000000 0.38651842970525

0.95000000000000 0.44322513172968

1.00000000000000 0.50614014425799

 

MATLAB

 

 

Maple Mathcad

.

3. MATLAB m-:

function df=DifEq(t,x)

global a k

df=(exp(k*x+t)-exp(-(k*x+t)))/(2.0*(0.9+a))+k*x;

:

. .





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