odem()

function odem()
% Simple and ilustrative script to show the use of ODE function to
% solve ordinary differential equations.
% The classic example of the Van der Pol oscilator was used here.
% The script shows two plots; the time response and the phase plane for
% different initial conditions depending on the coordinates of the mouse
% pointer.

init = [0 0];   % Initial Conditions vector 
initt = 0;      % Timespan
finalt = 20;
butt=1;
while ((isempty(init))) || (butt ~=3)  % Right click ends script. 
    [T Y]=ode45(@vdp1,[initt finalt],init);  % Use of ode45 ('help ode45');
    figure(2);
    plot(T,Y); xlabel('time');title('Time Response');
    legend('x','xdot',2);
    figure(1);
    plot(Y(:,1),Y(:,2));xlabel('x');ylabel('xdot'); title('Phase Plane');
    hold on;
    [initx inity butt]=ginput(1);
    init=[initx inity];
end
close(1);close(2);
end

function Xdot=d_eq(t,X) % Differential Equation Definition 
%(if ode1.m is not installed, see 'help ode45')
x=X(1); % Variable vectors
y=X(2);
        % Van der Pol differential equation:
Xdot(1)=y;
Xdot(2)=(1-x^2)*y-x;  

Xdot=Xdot'; % Result vector
end