First-Order Equations · Superchallenge problem

A tank drains so that its volume $y(t)\ge0$ satisfies $y'=-(1+t)\sqrt{y}$ for all $t\ge0$, with $y(0)=4$, and $y$ is differentiable on $[0,\infty)$. Find $\displaystyle\int_0^\infty y(t)\,dt$.