       Re: Piecewise with ODE and constant

• To: mathgroup at smc.vnet.net
• Subject: [mg104862] Re: [mg104722] Piecewise with ODE and constant
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Thu, 12 Nov 2009 06:02:15 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200911081141.GAA24486@smc.vnet.net>

```You don't have a differential equation (yet) in eq.  Did you intend the
equation to be:

v'[t] (1/c) (i - v[t]/r) == 0

?

Becky wrote:
> I have tried so many different ways to do this problem, that I am stuck.
> Its like being back I school.
>
> I would like to plot my ODE which is a curve that goes starts at 10 msec and
> ends at 100 msec).  In the beginning there is no current delivered to the
> cell until time equal 10 msec.  Once the current probe in inserted to the
> cell, I have a ODE, which is modeled as an RC circuit.  When time equal 100
> msec, the current it turned off, and the curve should go back to the
> original state.  I have tried using If statements, Piecewise plots, and so
> on, but I cannot get the curve to work with the initial and final conditions
> of -70 mV.
>
> I would like to stay with solving the ODE using Dsolve, vs., NDSolve, if
> that is ok.  I cannot figure out my problem, I need help, please.
>
> Sincerely Yours
> Prof. Jake
>
>  eq=v'[t]*1/c *(i-v[t]/r)
>
>  r=100 x 10^6;i=0.3 x 10^-9;c=100 x 10^-12;
>
>  ans=DSolve[{eq,v==0},v[t],t]
>
>  p1=Plot[v[t]/.ans,{t,0,140 x 10^-3}]
>
>  Plot[Piecewise[{{-70 x 10^-3,0*t*10 x 10^-3},{ans,10 x 10^-3*t*100 x 10^-3},{-70 x 10^-3,100 x 10^-3*t*140 x 10^-3}}],{t,0,140 x 10^-3}]
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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