Valery,
The other solvers will probably work with units in a semi-fashion if you make the initial values dimensionless by dividing by their default units. The results will appear dimensionless also, so the units need to be reattached to the output. I got the first two solvers to work but didn't go on to the others.
So the state is half there regarding units. The derivative functions (your "f") can now have dimensions and they can be different, but not the initial values and results. The initial values can have dimensions provided they are all the same.
These results are similar to the sbval situation discussed earlier.
Harvey