How to solve multivariable ODE

I have the equations:

dx/dt = 2 - 0.09x + 0.038y

dy/dt = 0.066x - 0.038y

x(0) = 0

y(0) = 0

Ultimately I need to solve the ODE and plot for x and y versus time (t). I just don't know how to code for the equations in Matlab.

Thanks

Answer 1

[Manvi Goel]

In order to solve for a system of differential equations, you could use the dsolve function. You can refer to this link which explains the implementation with an example:

https://in.mathworks.com/help/symbolic/solve-a-system-of-differential-equations.html

Answer 2

[Alan Stevens]

If you don't have the symbolic toolbox available you could just do something like the following

% Define gradient function where X(1) = x and X(2) = y
dXdt = @(t,X) [2 - 0.09*X(1) + 0.038*X(2); 0.066*X(1) - 0.038*X(2)];

% Set your timespan
tspan = [0 1];  % Modify as desired

% Set your initial conditions IC = [x(t=0)  y(t=0)]
IC = [0 0];

% Call ode solver
[t, X] = ode45(dXdt, tspan, IC);

% Extract x and y
x = X(:,1);
y = X(:,2);

% Plot results
plot(t,x,t,y),grid
legend('x','y')