I used the euler scheme to approximate the solution of the IVP $$\frac{du}{dt} = \frac{8e^{-t}}{2\pi u^2 \cos(\pi t/2)}, \qquad u(t_0) = 0.4$$ on the interval $I = [0,5]$. However, the method failed to approximate a solution and obtained "$\mathtt{Inf}$" at some point in the interval.
I don't understand the reason why the method failed. Could you please help me?