function f(x, y :double) :double;
begin
  f := 2*x*x + 3*x*y + y*y + 3*x + 2*y - 1;
end;

procedure TForm1.Button1Click(Sender: TObject);
var x, y, y1, k1, k2, k3, k4, h, he :double;
    fe : array[1..4] of double;
    i :integer;
begin
  h := 0.000001;
  x := 0;
  y := -1;
  y1 := -1;

  y := y1 + h*f(x, y) + 2*h;
  y1 := y;
  x += h;
  Memo1.Lines.Add('Метод Эйлера: ');
  while (x < 1-h) do
  begin
    y := y1 + h*f(x, y);
    y1 := y;
    if ((trunc(x*1E6) = 2E5) or (trunc(x*1E6) = 4E5) or
        (trunc(x*1E6) = 6E5) or (trunc(x*1E6) = 8E5)) then
    begin
      Memo1.Lines.Add('x= '+FloatToStrF(x, ffFixed, 0, 8));
      Memo1.Lines.Add('y='+FloatToStrF(y, ffFixed, 0, 8));
    end;
    x += h;
  end;

  x := 0;
  y := -1;
  y1 := -1;
  Memo2.Lines.Add('Метод Рунге-Кутты: ');
  while (x < 1-h) do
  begin
    k1 := f(x, y1);
    k2 := f(x+h/2, y1+(h/2)*k1);
    k3 := f(x+h/2, y1+(h/2)*k2);
    k4 := f(x+h, y1+h*k3);
    y := y1 + (h/6)*(k1+2*k2+2*k3+k4);
    y1 := y;
    x += h;
    if ((trunc(x*1E6) = 2E5) or (trunc(x*1E6) = 4E5) or
        (trunc(x*1E6) = 6E5) or (trunc(x*1E6) = 8E5)) then
    begin
      Memo2.Lines.Add('x= '+FloatToStrF(x, ffFixed, 0, 8));
      Memo2.Lines.Add('y='+FloatToStrF(y, ffFixed, 0, 8));
    end;
  end;

  x := 0;
  y := -1;
  y1 := -1;
  i := 1;
  he := -0.001;
  while (x > -1+he) do
  begin
    k1 := f(x, y1);
    k2 := f(x+he/2, y1+(h/2)*k1);
    k3 := f(x+he/2, y1+(h/2)*k2);
    k4 := f(x+he, y1+h*k3);
    y := y1 + (h/6)*(k1+2*k2+2*k3+k4);
    y1 := y;
    if ((floor(abs(x)*1E6) = 2E5) or (floor(abs(x)*1E6) = 4E5) or
        (floor(abs(x)*1E6) = 6E5) or (floor(abs(x)*1E6) = 8E5)) then
    begin
      fe[i] := y;
      inc(i);
    end;
    x += he;
  end;

  x := 0;
  y := -1;
  y1 := -1;

  Memo3.Lines.Add('Метод Адамса: ');
  while (x < 1-h) do
  begin
    y := y1 + (h/24)*(55*fe[1] - 59*fe[2] + 37*fe[3] - 9*fe[4]);
    y1 := y;
    if ((trunc(x*1E6) = 2E5) or (trunc(x*1E6) = 4E5) or
        (trunc(x*1E6) = 6E5) or (trunc(x*1E6) = 8E5)) then
    begin
      Memo3.Lines.Add('x= '+FloatToStrF(x, ffFixed, 0, 8));
      Memo3.Lines.Add('y='+FloatToStrF(y, ffFixed, 0, 8));
    end;
    x += h;
  end;
end;