The equation , gives us some trouble.
warning on % ignore this line
f = @(t,u) (t+u).^2;
[t,u] = ode45(f,[0,1],1);
Warning: Failure at t=7.853789e-01. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.776357e-15) at time t.
semilogy(t,u)
xlabel('t'), ylabel('u(t)'), title('Finite time blowup')
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.