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DSolve does not solve a differential. No error message either.

Posted 9 years ago


I tried to solve a differential equation by using DSolve. I set up the equation and executed it, but Mathematica just output the differential equation again without any error message. Does anyone know what happened? How could I solve this differential equation?

   DSolve[{V'[t]==A ?p (V0 + g t- V[t]) Exp[B (Vg - V[t])] -kr  V[t],V[0]==0},V[t],t]
POSTED BY: Dawei Heh
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When DSolve cannot find a solution it will return unevaluated. Do you expect that there should be an analytic solution?

Do you need an analytic solution? If not, then make use of NDSolve with numerical values of your parameters.

POSTED BY: David Reiss

If you need a symbolic approximation, there are a lot of things you can try:

For example, try to linearize the equation or a linear approximation to the problematic parts of the equation. If V[t] stays near 0, then then

Exp[B (Vg - V[t])]

Is reasonably well approximated by:

Normal@Series[Exp[B (Vg - V[t])], {V[t], 0, 1}]

E^(B Vg) - B E^(B Vg) V[t]

Substituing this in will give you an answer.

For more accurate approximations, try using the method of perturbations.

POSTED BY: Sean Clarke
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