% Matlab diary from cs110a, Feb 28 2005.
%
% This is what I typed in class.  
%
% Type it into Matlab yourself to
% reproduce the output I showed.

help ode45
clf
[T,Y] = ode45(@lve, [0 20], [300; 150]);
size(T)
size(Y)
plot(T,Y)
T(1:10)
Y(1:10,:)
plot(Y(:,1), Y(:,2)); xlabel('rabbits');ylabel('foxes');title('Phase Plot')
edit f
type f

function ydot = f(t,y)
% F  :  function ydot = f(t,y) for ODE solution
%
%   t:  scalar time
%   y:  vector, y = y(t), unknown function
%   
%   ydot:  vector of dy / dt
ydot = [y(2) ; -y(1)];

clc
ode45(@f, [0 10], [1 ; 0]);
legend('x(t)', 'xdot(t)');

edit f
type f

function ydot = f(t,y)
% F  :  function ydot = f(t,y) for ODE solution
% falling object
%
%   t:  scalar time
%   y:  vector, y = y(t), unknown function
%   
%   ydot:  vector of dy / dt
ydot = [y(2) ; -1 + (y(2))^2];

ode45(@f, [0 2], [1 ; 0]);
legend('height of object', 'speed of object')