how to solve matrix form differential equations using ODE45?

The equation is as above.

The initial values are X0 , Y0 = 30

Time range is 1 to 1000s

How should I write the code?

a,b are constants.

[James Tursa]

Is the left hand side supposed to simply be a1*X' for the first equation and b1*Y' for the second equation?

[yonghyeok lee]

a_1 , b_1 is constants.

The Equation can be expressed

X' means dx/dt

Y' means dy/dt

Answer 1

[Jan]

y0     = [30; 30];
tspan  = [1, 1000];
[t, y] = ode45(@YourODE, tspan, y0);
plot(t, y);

function dy = YourODE(t, y)
a1 = 2;   % set accordingly
a2 = 3;
b1 = 4;
b2 = 5;
X = y(1);
Y = y(2);

dy = [-X / a1 + Y / a1 + a2 / a1; ...
       X / b1 - Y / b1 + b2 / b1];
% Or:
% dy = [(-X + Y + a2) / a1; ...
%       ( X - Y + b2) / b1];

% Or:
% dy = [-1/a1, 1/a1; 1/b1, -1/b1] * y + [a2/a1; b2/b1];
end