function Lab5
clear all; close all; clc;

    function dy=myODE(t,y)
    dy1=y(2); %y_1' = y_2
    dy2=-sin(y(1)); 
    dy=[dy1;dy2];
    end

% initial conditions y(0)=y0_1 and y'(0)=y0_2
y0=[-1; 2];
% time interval
t=0:0.1:5;

% Solving the ODE for different values of the parameters
%%%% Try different values for k and m to answer the questions in your lab

[t,y1]=ode45(@myODE, t, y0);

figure
% a positive and a negative evalues
[x,y]=meshgrid(-7:.2:7,-5:.2:5);
dx= y; 
dy=  -sin(x); 
dyu=0.5*dy./sqrt(dy.^2+dx.^2);
dxu=0.5*dx./sqrt(dy.^2+dx.^2);
quiver(x,y,dxu,dyu)
hold on
plot(y1(:,1),y1(:,2), 'LineWidth',2)
xlabel('x')
ylabel('y')


%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Uncomment when solving the Food Chain Problem
% % Matrix
% A=[[1,2,3];[5,6,7];[0,1,0]]
% % Finds eigenvalues and eigenvectors of A
% [V,D]=eig(A)

end