Simultaneous Calculation of Mass Matrix and Driving Function

I am using the ODE solver to solve a set of coupled differential equations of the form Mx = F.

I would like to be able to simultaneously calculate M and F for two reasons:

(1) There are several shared calculations for both elements that are currently duplicated in the two independent functions for enhanced numerical efficiency.

(2) I am having scaling issues with some of the rows of the system (e.g. the nominal values in the matrix differ by orders of magnitude). By simultaneously calculating M and F, I could normalize the diagonal of the mass matrix, adjusting the other elements of that row in both M and F.

Can this be done using the ODExx series of functions? Thanks.