我偶然发现了这个matlab代码可以解决这个问题

y'''(t) + a y(t) = -b y''(t) + u(t)

但是我对ode_system函数定义感到困惑，特别是y(2) y(3)部分。
ode_system函数中的y(2) y(3)部分让我很困惑，它对总体解决方案有何贡献

% Define the parameters a and b
a = 1;
b = 2;
    
% Define the time horizon [0,1]
time_horizon = [0, 1];
    
% Define the initial conditions for y, y', and y''
initials = [0; 0; 0];
    
% Define the function handle for the input function u(t)
%sin(t) is a common example of a time-varying function.
% You can change the definition of u to any other function of time,
% such as a constant, a step function, or a more complex function, depending on your needs
    
u = @(t) sin(t);
    
% Define the function handle for the system of ODEs
odefunction = @(t, y) ode_system(t, y, a, b, u);
    
% Solve the ODEs using ode45
[t, y] = ode45(odefunction, time_horizon, initials);
    
% Plot the solution
plot(t, y(:,1), '-', 'LineWidth', 2);
xlabel('t');
ylabel('y');
    
function dydt = ode_system(t, y, a, b, u)
    
%Define the system of ODEs
    
dydt = [y(2); y(3); -b*y(3) + u(t) - a*y(1)];
    
end