\[
2X_1 \longrightarrow X_2 \quad \mbox{and} \quad X_2 \longrightarrow 2 X_1
\] with propensities \(h_1(X_1, X_2) = 0.5 k_1 X_1(X_1-1)\) and \(h_2(X_2) = k_2 X_2\)

### Moment equations

The equation for the mean ODE is \[
\frac{dE[X_1]}{dt} = 0.5 k_1 (E[X_1^2] - E[X_1]) -k_2 E[X_1]
\] and second moment \[
\frac{dE[X_1^2]}{dt} = k_1 (E[X_1^2X_2] - E[X_1 X_2]) + 0.5 k_1(E[X_1^2] - E[X_1])
k_2 (E[X_1] - 2 E[X_1^2])
\] where \(E[X_1]\) is the mean of \(X_1\) and \(E[X_1^2] - E[X_1]^2\) is the variance