Writing a system of differential equations with the given arbitrary reactions We have the following elementary reactions:
\begin{align}
&amp;\overset{k_1}{\longrightarrow}A\overset{k_2}{\longrightarrow}{B+C}\\
&amp;C \overset{k_4}{\longrightarrow} 2D \overset{k_5}{\longrightarrow}{C}\\
&amp;B \overset{k_3}{\longrightarrow}\\
&amp;D \overset{k_6}{\longrightarrow}
\end{align}
Let $\alpha(t), \beta(t), \gamma(t), \delta(t)$ denote the concentrations of $A, B, C, D$, respectively.
\begin{align}
\frac{\mathrm d}{\mathrm dt}\alpha(t) &amp;= k_1 - k_2\alpha(t)\\[3pt]
\frac{\mathrm d}{\mathrm dt}\beta(t) &amp;= k_2\alpha(t) - k_3\beta(t)\\[3pt]
\frac{\mathrm d}{\mathrm dt}\bigl(2\delta(t)\bigr) = 2\frac{\mathrm d}{\mathrm dt}\delta(t) &amp;= k_4\gamma(t)-k_6\delta(t)^2 \quad \text{or} \quad \frac{\mathrm d}{\mathrm dt}\delta(t) = \frac{k_4}{2}\gamma(t) - \frac{k_6}{2}\delta(t)^2\\[3pt]
\frac{\mathrm d}{\mathrm dt}\gamma(t) &amp;= k_5\delta(t)^2 - k_4\gamma(t) + k_2\alpha(t)\\
\end{align}
Is my systems of equations correct?
$\displaystyle\frac{\mathrm d}{\mathrm dt}\alpha(t) = k_1 - k_2\alpha(t)$ is correct.

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

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