How to get the function after solving the differential equation using Eulers method?

How to get the value of x1(t) and x2(t) from the set of equations?

Initial condition is x1=1 and x2=2

x1dot=x1 -x2;

x2dot=-x1+x2;

Answer 1

[Sergey Kasyanov]

Hello!

A = [1, -1
     -1, 1];
x0 = [1
      2];
dx = [0
      0];
time_step = 0.1;
time = 0 : time_step : 10;
x = [x0, nan(2, time(end) / time_step)];
%solving
for i = 1:size(x, 2)-1
    dx = A*x0; %matrix form of equation system
    x(:, i+1) = x(:, i) + time_step*dx;
end

% plot results
figure; hold on;
plot(time, x(1,:), 'DisplayName', 'X1');
plot(time, x(2,:), 'DisplayName', 'X2');
xtitle('time');
legend show