There are over 50 equations in the PDF, and the ODEs appear in various places. Most forum users don't have the time to read the entire paper and identify which set of ODEs to solve, especially users who are not experts in the film-boiling chemical vapor infiltration process.
You can find examples in the ode45 documentation and follow them to write the MATLAB code for your application. Afterward, post the code so that we can troubleshoot any errors that may arise.
I used the first example here, the popular Van der Pol oscillator in the Electrical Engineering world. They are just a few lines. But the length of the ODE function (odefun) depends on the size of the system that you want to solve.
%% Use ode45 to solve ODEs on time span [0 20] with initial values [2 0]
[t, y] = ode45(@odefun, [0 20], [2; 0]);
%% Plot the results
plot(t, y(:,1), '-o', t, y(:,2), '-o')
%% Labels
title('Solution of van der Pol Equation (\mu = 1) with ODE45');
xlabel('Time t'), ylabel('Solution y'), legend('y_1', 'y_2')
%% ODEs of Van der Pol oscillator
function dydt = odefun(t,y)
dydt = [y(2);
(1 - y(1)^2)*y(2) - y(1)];
end
