% function to specify the set of ODEs to be integrated by ode45
%
function dy = vanderpol(t,y)           %vanderpol will be the name of the 
                                       %function to be called by 1st argument
                                       %of ode45

dy = zeros(2,1);                       %this says that dy is a vector of 2
                                       %components and initialize them to 
				       %zero

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      % The system of equations being implemented for      %
      % undamped pendulum example below is 	           % 
      %							   %
      %            dy(1) 				   %
      %            ----  = y(2) 			   %
      %             dt					   %
      %							   %
      %							   %
      %            dy(2)				   %
      %            ----- = -omega^2*sin(y(1))    	   %
      %             dt					   %
      %							   %
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Begin specifying set of ODEs
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% PUT HERE your own ODEs for problem set 3.

omega = 1.0;                           %this is a parameter of the set of ODEs
                                       %which is omega, being set to 1.0
dy(1) = y(2);
dy(2) = -omega*omega*sin(y(1));