Error using plot Vectors must be the same length.

Every time I run this code, I get "Error using plot Vectors must be the same length.

function f = lab_8( x , y)
     f = ((x.^2)*cos(y) + 0.1);
end



function [x,y] = lab_8_method_2(f, y0, sp, h)
     x = sp(1):h:sp(2);
     y = y0;

     for n =1:length(x)-1
         x(n) = (n-1)*h;
         y(n+1) = y(n)+h*(0.75*f(x(n),y(n))+...
                  0.25*f(x(n)+h/0.5,y(n)+... 
                  (h/0.5)*f(x(n),y(n))));
     end
end




function [x,y] = lab_8_method_4(f, y0, sp, h)
     x = sp(1):h:sp(2);
     y = y0;

     for n=1:length(x)-1
         k1=f(x(n) , y(n));
         k2=f(x(n)+h/2 , y(n)+h*k1/2);
         k3=f(x(n)+h/2 , y(n)+h*k2/2);
         k4=f(x(n)+h , y(n)+h*k3);
         dy= h*(k1+2*k2+2*k3+k4) / 6;
         y(n+1) = y(n) + dy;
     end
end



[x, y2] = lab_8_method_2(@lab_8, 0.3, [0 1 ], 0.01);
plot(x, y2 ,'r'); hold on;

[x, y4] = lab_8_method_4(@lab_8, 0.3, [0 1], 0.01);
plot(x, y4, 'b'); hold on;

qn = dsolve('Dy = (x.^2)*cos(y) + 0.1', 'y(0) = 0.3');
syms t
v = subs(qn, [t], [x]);
a = eval(v); plot(x,a,'y'); hold off;
legend('2-го порядку', ' 4-го порядку', ' Точна відповідь');

T=table(x(:), y2(:), y4(:), a(:));
T.Properties.variableNames = {'xi','Рунге-Кутта 2-го порядку','Рунге-Кутта 4-го порядку', 'Точна відпоівдь'}

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Answer 1

[Jan]

[x, y2] = lab_8_method_2(@lab_8, 0.3, [0 1], 0.01);
plot(x, y2 ,'r'); hold on;

[x, y4] = lab_8_method_4(@lab_8, 0.3, [0 1], 0.01);
plot(x, y4, 'bo'); hold on;

qn = dsolve('Dy = (x.^2)*cos(y) + 0.1', 'y(0) = 0.3');

Warning: Support of character vectors and strings will be removed in a future release. Use sym objects to define differential equations instead.

Consider this warning.

syms t
v = subs(qn, t, x);
a = eval(v);
size(x)

ans = 1×2

1 101

size(a)

ans = 1×2

1 10201

This is the problem. x is a row vector with 101 elements. The equation is defined as CHAR vector. t is symbolic, but you substitute it by a numerical vector. The equation does not contain a "t", but only y and x, so substituting t is not meaningful.

Read the examples of dsolve again and rewrite the symbolic part.

plot(x,a,'y'); hold off;

Error using plot
Vectors must be the same length.

function f = lab_8(x , y)
f = x.^2 * cos(y) + 0.1;
end

function [x,y] = lab_8_method_2(f, y0, sp, h)
x = sp(1):h:sp(2);
y = y0;
for n = 1:length(x)-1
   x(n)   = (n-1)*h;
   y(n+1) = y(n)+h*(0.75*f(x(n),y(n))+...
         0.25*f(x(n)+h/0.5,y(n)+... 
         (h/0.5)*f(x(n),y(n))));
end
end

function [x,y] = lab_8_method_4(f, y0, sp, h)
x = sp(1):h:sp(2);
y = y0;
for n=1:length(x)-1
    k1 = f(x(n) , y(n));
    k2 = f(x(n)+h/2 , y(n)+h*k1/2);
    k3 = f(x(n)+h/2 , y(n)+h*k2/2);
    k4 = f(x(n)+h , y(n)+h*k3);
    dy = h*(k1+2*k2+2*k3+k4) / 6;
    y(n+1) = y(n) + dy;
end
end