% SlopeField.m
% MST 383/683 
% Fall 2020

% Script calculating and plotting the direction field of the DEs: 

clear, clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% y' = y
[t,y] = meshgrid(-2:0.5:2, -2:0.5:2);

f1 = ones(size(y));
f2 = y;

quiver(t,y,f1,f2)
hold on
t_vec = -2:0.01:1;
y1 = exp(t_vec);
y2 = -exp(t_vec);
plot(t_vec,y1,'k','LineWidth',2)
plot(t_vec,y2,'b','LineWidth',2)
xlabel('t')
ylabel('y')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% y' = 2ty^2
clear
[t,y] = meshgrid(-1:0.2:1, 1:0.5:4);

f1 = ones(size(y));
f2 = 2*t.*(y.^2);

figure
quiver(t,y,f1,f2)
hold on
t_vec = -0.87:0.01:0.87;
y1 = 1./(1-t_vec.^2);
plot(t_vec,y1,'k','LineWidth',2)
xlabel('t')
ylabel('y')
axis([-1.1 1.1 1 4.5])