function ydot = sect_5_1_ode_fn(t,y)
% SECT_5_1_ODE_FN_PART_A - returns the time derivative needed to integrate the covariance evolution equations 
%
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% some parameters:
omega_n = 10;
zeta = 0.3;
q = 10;

% extract the components:
y = y(:); 
p11 = y(1);
p12 = y(2);
p22 = y(3);

ydot = zeros(3,1);
ydot(1) = 2*p12;
ydot(2) = -( omega_n^2 )*p11 - 2 * zeta * omega_n * p12 + p22;
ydot(3) = -2*( omega_n^2 )*p12 - 4 * zeta * omega_n * p22 + q;