@Cola, let's correct your Simulink model first.
The ODE is given by
which can be rearranged into
Integrating both sides and 
is obtained:
is obtained:
Technically it means that the signal after the integrator block (1/s) is 
, and that is the output of the system.
, and that is the output of the system.To obtain 
, you need to properly get the integrand, a function that is to be integrated:
, you need to properly get the integrand, a function that is to be integrated:
So you should perform the subtraction first, and then it multiply with 
using the Gain block. The signal from the Gain block is fed into the Integrator block (1/s).
using the Gain block. The signal from the Gain block is fed into the Integrator block (1/s).If 
, then the MATLAB code looks something like this:
, then the MATLAB code looks something like this:tau = 1;
% 1st-order Ordinary differential equation
fcn = @(t, x) [(1 - x)/tau];
tspan = [0 10];
init = 0; % initial condition
% Runge-Kutta Dormand-Prince 4/5 solver
[t, x] = ode45(fcn, tspan, init);
plot(t, x)
grid on
xlabel('t')
ylabel('a(t)')
title('Time response of the system')
Result:
