2.Программа:

uses crt;

const n=10;

var

x: array[0..n] of real;

y: array[0..n] of real;

y_t: array [0..n] of real;

a,b,h,k1,k2:real;

j: integer;

Begin clrscr;

a:=Pi/2; b:=(Pi/2)+1;

h:=(b-a)/n;

y[0]:=pi;

x[0]:=pi/2;

for j:=0 to n do begin

x[j]:=a+h*j;

k1:=y[j]/(x[j])+(sin(x[j])*x[j]);

k2:=(y[j]+h/2*k1)/(x[j]+h/2)+(sin(x[j]+h/2)*(x[j]+h/2));

y[j+1]:=y[j]+h*k2; end;

for j:=0 to n do begin

y_t[j]:=-(x[j])*cos(x[j])+2*x[j]; end;

writeln('n y_v y_t raznost');

for j:=0 to n do writeln( y[j]:6:3,' ',y_t[j]:6:3, ' ' , (y_t[j]-y[j]):9:8);

readln;

end.

3.Результаты:

Turbo Pascal Version 7.0 Copyright (c) 1983,92 Borland International

'n y_v y_t raznost

3.142 3.142 0.00000000

3.508 3.508 0.00007848

3.893 3.893 0.00012362

4.294 4.294 0.00013388

4.709 4.709 0.00010843

5.134 5.134 0.00004712

5.567 5.567 -0.00004954

6.005 6.004 -0.00018049

6.443 6.443 -0.00034408

6.878 6.877 -0.00053820

7.306 7.305 -0.00076027

4.Результаты:

Turbo Pascal Version 7.0 Copyright (c) 1983,92 Borland International

'n y_v y_t raznost

3.142 3.142 0.00000000

3.893 3.893 0.00051009

4.709 4.709 0.00049358

5.567 5.567 -0.00007103

6.443 6.442 -0.00116465

7.308 7.305 -0.00273330

5.Вывод :

 Чем меньше шаг на отрезке, тем ближе решение к истинному.