= Solution
First retain the equilibrium solution $\boxed{y\equiv0}$. Any nonzero real solution has constant sign on its interval of existence, since the polynomial right-hand side is <locally Lipschitz> and <Picard-Lindelöf theorem> prevents crossing the zero solution.
For a nonzero solution, the <Bernoulli differential equation> substitution $u=y^{-4}$ gives
$$
u'=-4y^{-5}y'=-8u-16.
$$
This <linear ordinary differential equation> has solution $u+2=Ce^{-8x}$. Therefore every nonzero real solution is
$$
\boxed{y(x)=\pm\bigl(Ce^{-8x}-2\bigr)^{-1/4},\qquad C>0,\quad x<\frac18\ln\frac C2.}
$$
Either sign may be chosen and remains fixed. The restriction ensures $y^{-4}>0$; nonpositive $C$ gives no nonzero real solution. These are maximal real intervals, and their restrictions are also solutions. As the right endpoint is approached, $|y|$ diverges in <finite-time blowup>. The substitution would have lost $y=0$ if it had not been checked separately.
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