The general first order ODE invariant under X
X rewritten in the gauge xi=0
If the ODE is given, its right hand side is used to replace the highest derivative (in this example the ODE is of first order).
So, the above is just the original symmetry X rewritten in the gauge xi=0. Let's test this result.
The general form in which X above can be rewritten is as follows:
where _F2(x, y) is an arbitrary function of its arguments, introduced by Xgauge. This result can be tested as well.