Demonstrate that the initial value problem
\begin{equation*}
y^3y' +t=0,\qquad y(0)=0
\end{equation*}
does not have a solution on any interval $(\alpha,\beta)$, where $\alpha<0<\beta$, and explain why this fact does not contradict the existence and uniqueness theorem for first order initial value problems (Theorem 2.4.2 in the textbook).
