[firedrake] Solving an ODE in firedrake

Hi all, Say I have some ODE of the following: dc/dt = f where f is some analytical expression. So if I used backward euler temporal discretization: (c - c0)/dt = f where c, c0, and f belong to the same function space (P1 lagrange elements). My question now is, is it a good idea to solve the above using the Galerkin weak form? So if I had something like: a = w*c*dx L = w*(dt*f + c0)*dx Would this give an accurate solution? Or is there a better way of solving this ODE? Thanks, Justin