The subject is a bit cryptic, I know, but here is what I'd like to do: Let's say I am solving an ODE like this:

    s = DSolve[{x'[t] == 1, y'[t] == x[t] t, x[0] == x0, 
       y[0] == y0}, {x[t], y[t]}, t]

which gives

    {{x(t)->t+x0,y(t)->1/6 (2 t^3+3 t^2 x0+6 y0)}}

I could then apply the new rule to the second one that comes out of the `DSolve` to obtain `y[t]` as a function of `x[t]`.

Now I'd like to convert the first of the replacement rules with one that replaces `t`, so the rule should look like this:

    t -> -x0 + x[t]

I think the way to accomplish this would be to convert the Head `Rule` of my first rule to an `Equal`, and feed that into `Solve`. I tried to do that, but I can't get this to work.