clear
format compact

%%
% The equation u'=(u+t)^2, gives us some trouble.
warning on

f = @(t,u) (t+u).^2;
[t, u] = ode45(f, [0,1], 1);

semilogy(t, u)
xlabel('t')
ylabel('u(t)')
title('Finite time blowup')
grid on

%%
% The warning message we received can mean that there is a bug in the
% formulation of the problem. But if everything has been done correctly, it
% suggests that the solution does not exist past the indicated
% time.