Writing a system of differential equations with the given arbitrary reactions
$\displaystyle\frac{\mathrm d}{\mathrm dt}\alpha(t) = k_1 - k_2\alpha(t)$ is correct.

Just to show you the way, here are the next equations:

$$
\begin{align}
\frac{\mathrm d}{\mathrm dt}\beta(t) &amp;= k_2\alpha(t) - k_3\beta(t) \\
\frac{\mathrm d}{\mathrm dt}\gamma(t) &amp;= k_2\alpha(t) - k_4\gamma(t) + k_5\delta(t)^2 \\
\frac{\mathrm d}{\mathrm dt}\delta(t) &amp;= 2k_4\alpha(t) - k_6\delta(t) - k_5\delta(t)^2 
\end{align}
$$