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Re: Piecewise with ODE and constant
*To*: mathgroup at smc.vnet.net
*Subject*: [mg104770] Re: Piecewise with ODE and constant
*From*: sean <sean_incali at yahoo.com>
*Date*: Mon, 9 Nov 2009 05:45:33 -0500 (EST)
*References*: <hd6c4q$p43$1@smc.vnet.net>
> eq=v'[t]*1/c *(i-v[t]/r)
This is not an equation. DSolve requires an equation.
v[t]==v[t] for instance.
> r=100 x 10^6;i=0.3 x 10^-9;c=100 x 10^-12;
>
x is not multiplication. * is used instead. So r= 100*10^6
> ans=DSolve[{eq,v[0]==0},v[t],t]
>
> p1=Plot[v[t]/.ans,{t,0,140 x 10^-3}]
Again x is not multiplication. 140*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}]
I'm not sure what you want above. If you want to define an ode
piecewise then you have to define is like this. But what yousaid you
want is i0[t_]:= i0[t]/; 10 <= t <= 100;
i0[t_] := 0/; t < 0;
i0[t_] := 0/; 0 <= t <= 10;
i0[t_] := 1/; 10 <= t <= 100;
deqn = i0[t] == v[t]/r + c v'[t];
NDSolve will solve that.
On Nov 8, 4:04 am, "Becky" <noslow... at comcast.net> 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 t he
> 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}]
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