% Plot the vector fields for three different ODE's

close all
clear all

%*** y'(t) = y(t) --> y(t) = exp(t) + y0 
tmax = 5;
ymax = 5;
tVec = linspace(0,tmax,10);
yVec = linspace(0,ymax,10);
tPlot =linspace(0,tmax,101);

f = @(t,y) 0.5*y;

figure(1)
% plot the vectorfield using the vectors tVec an yVec

ylim([0,ymax]); xlim([0,tmax])
title('y(t) = 0.5*y(t)')

%*** y'(t)  = y^2+t^2
tmax = 2;
ymax = 3;
tVec = linspace(0,tmax,10);
yVec = linspace(0,ymax,10);
tPlot =linspace(0,tmax,101);

% define function f

figure(2)
% plot vectorfield

ylim([0,ymax]); xlim([0,tmax])
title('y(t) = y^2+t^2')

%*** y'(t)  = (5-5*y).*y
tmax = 2;
ymax = 2;
tVec = linspace(0,tmax,10);
yVec = linspace(0,ymax,10);
tPlot =linspace(0,tmax,101);

% define function f

figure(3)
% plot vectorfield

ylim([0,ymax]); xlim([0,tmax])
title('y(t) = (5-5*y).*y')