Help w DSolve or NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg24211] Help w DSolve or NDSolve
• From: Chimba Mkandawire <bluntme at u.washington.edu>
• Date: Fri, 30 Jun 2000 01:57:38 -0400 (EDT)
• Organization: University of Washington
• Sender: owner-wri-mathgroup at wolfram.com

```Hello Mathematica guru's, I'm running into problems with Mathematica 4.0.1
running on a P3 500. I've got an ode representing motion of a nonlinear
spring in series to a linear dashpot/nonlinear spring parallel combination.

Here's the code.

In[1]:= eq1 = F[t] + A + G/D/C*F'[t] Log[F[t]/C +1.] == G*V + A/(F[t]/C +1.)
* Exp[B*V*t - 1./D)

This equation is implicit, so I know DSolve shouldn't have any problems
solving this with algebraic methods (if possible).

In[2]:= DSolve[eq1, F[t],t]

Mathematica will think for a while, then output my input. No error messages.
I'll try a different approach, I have V and V*t as my driving functions. I
want to try to solve the hold case, where velocity V is zero. This way, the
ode becomes explicit.

In[3]:= eq3 = F[t] + A + G/D/C*F'[t] Log[F[t]/C +1.] == A/(F[t]/C +1.) *
Exp[B*V*t - 1./D)

I define an initial condition.
In[4]:= ic2 = F[0.] == 100.

In[5]:= DSolve[{eq3,ic2},F[t],t]
Out[5]:= DSolve[F[t] + A + G/D/C*F'[t] Log[F[t]/C +1.] == A/(F[t]/C +1.) *
Exp[B*V*t - 1./D), F[0.]==100.},F[t],t]

??What gives?? I'll try NDSolve, if I'm not mistaken, that requires an
explicit formulation.

In[6]:= NDSolve[{eq3, ic2},F, {t,0.,4.}]
NDSolve::ndnum: Encountered non-numerical value for a derivative
at t==2.84273`*^-316
Out[6]:= {{F->InterpolatingFunction[{{0.,0.}},<>]}}

Does this mean that I need to use numbers for my coefficients? I can't
replace those coefficients with numbers until I can solve the DiffEq, then
curve fit my data to the solution.