% Let Romeo's love for Juliet at time t be R(t)
% Let Juliet's love for Romeo at time t be J(t)

% Problem 1
% R' = aJ  and  J'=-bR
a=1; b=1; c=11; d=1;

tspan =[0 20]; %domain under consideration
ic=[2 0]; % initial condition
dxdt = @(t,x) [a*x(1) + b*x(2); c*x(1)+d*x(2)]; 
% R is x(1); J is x(2)
[t, x] = ode45(dxdt, tspan, ic); 

%plot(t,x(:,1),'b')
plot(t,x(:,1),'b',t,x(:,2),'g')
xlabel('t', 'FontSize', 20)
ylabel( 'R(t), J(t)', 'FontSize', 20)
legend ({'R(t)', 'J(t)'}, 'FontSize', 18)
axis([0 20 -2.5 2.5 ])
grid on