System of differential equations can be solved in multiple ways. On the ways is to use dsolve function from Symbolic Math Toolbox.
Another way is to use ODE solvers:
Considering this example, y''+y'+y = sin(5*t) with ICs: y(0)=3, y'(0)=-2, follow the following steps to solve the equation.
Ys=@(t,y)([y(2);-(y(2)+3*y(1))+sin(5*t)]); % Define function
ICs = [3, -2]; % Define ICs
timespan = 0: pi/100:2*pi; % Define timespan
options_ODE = odeset('RelTol', 1e-6, 'AbsTol', 1e-8); % ODE Options
[t, y_ODE45]=ode45(Ys, timeSPAN, ICs, options_ODE); % Solve
Refer the following link for to know more about how to choose an ODE Solver.
