%% Question 3

%%
% Initial condition and time
x0 = 0.7233;
t0 = 0;

%% ode23
% Compute and plot the numerical solution using ode23
[t1,x1] = ode23(@(t,x)(1-x)*x-0.2, [t0,100], x0);
plot(t1,x1,'DisplayName','ode23');
hold on;
xlabel('t');
ylabel('x');
legend('Location','SouthEast');

%% ode15s
% Compute and plot the numerical solution using ode15s
[t2,x2] = ode15s(@(t,x)(1-x)*x-0.2, [t0,100], x0);
plot(t2,x2,'DisplayName','ode15s');

%% Analytical Solution
% Compute the analytical solution at 1001 points
t3 = linspace(0,100,1001);
x3 = sqrt(5)/10*tanh((t3-t0)*sqrt(5)/10+atanh((2*x0-1)*sqrt(5)))+0.5;
plot(t3,x3,'DisplayName','Analytical Soln.');
