# Solve a total derivative - independent vs. dependent variables

I am trying to force mathematica to solve a generally defined function for d lp:

In a reduced version, w depends on l2, lp and t. l2 and lp depend on t. Furthermore, w is constant with respect to t. So, I did

Solve[Dt[w[l2, lp, t], t] == 0, Dt[lp, t]]


which works.

The problem is that the dynamics of l2 do not depend on w, so they can be defined by:

l2[t_] := l20*E^(p*t)


where l20 is a constant. So, I tried the following:

l2[t_] := l20*E^(p*t)
Solve[Dt[w[l2, lp, t], t, Constants -> {l20, p}] == 0, Dt[lp, t]]


which did not help. Second try was this one,

Solve[Dt[w[l20*E^(p*t), lp, t], t, Constants -> {l20, p}] == 0, Dt[lp, t]]


which did not help either.

Does anybody have an idea?

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It might help to make l2 and lp explicitly function of t, inside that total derivative: Solve[Dt[w[l2[t], lp[t], t], t, Constants -> {l20, p}] == 0, Dt[lp[t], t]] – Daniel Lichtblau Oct 4 '13 at 14:01
It does. Thx. I will male the second question explicit in another question – Andreas Oct 10 '13 at 13:19

l2[t_] := l20*E^(p*t)