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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>
*Reply-to*: murray at math.umass.edu
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]==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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