While filling up a chemicals container at a constant rate of $300\,\rm L/min$, the crew of a naval ship discover two leakages at the bottom of the container. They discover that the chemical is leaking out of the first hole at a rate proportional to the square of the amount of chemical currently in the container while chemical is leaking out of the second hole at a rate proportional to the amount of chemical currently in the container.
The container already had $200\,\rm L$ of the chemical before they began filling. Let $t$ ($\rm min$) be the time since the crew started filling the container and let $C(t)$ be the number of litres of chemical in the container at time $t$.
Write down, but do not solve, the differential equation for $C(t)$ along with its initial condition.
So far I have
$$ \begin{align} \frac{\mathrm dW(t)}{\mathrm dt} &= W_\mathrm{in} - W_\mathrm{out} \\ W_\mathrm{out} &= kW^2 + W \end{align} $$
where $k$ is constant of proportionality. Therefore
$$\frac{\mathrm dW(t)}{\mathrm dt}= W_\mathrm{in} - kW^2 + W$$
Am I wrong? Can I get some help to complete?