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MathGroup Archive 2007

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Re: Simple ODE with time-dep BC

  • To: mathgroup at smc.vnet.net
  • Subject: [mg78022] Re: [mg77933] Simple ODE with time-dep BC
  • From: DrMajorBob <drmajorbob at bigfoot.com>
  • Date: Thu, 21 Jun 2007 05:52:17 -0400 (EDT)
  • References: <24202381.1182335834009.JavaMail.root@m35>
  • Reply-to: drmajorbob at bigfoot.com

The error message is perfectly clear:

> DSolve::dvnoarg : The function h appears with no arguments. More...

As for the second problem:

Once you've said u[t]=v^2, it makes no sense to solve for u[t] -- it's 
already known (and it doesn't solve the differential equation). But you 
can use a DIFFERENT t, say t0:

DSolve[{u'[t]/2 == -a*u[t] + c, u[t0] == v^2}, u[t], t]

{{u[t] -> (\[ExponentialE]^(-2 a t) (c \[ExponentialE]^(2 a t) -
       c \[ExponentialE]^(2 a t0) + a \[ExponentialE]^(2 a t0) v^2))/
    a}}

Bobby

On Wed, 20 Jun 2007 04:27:35 -0500, Apostolos E. A. S. Evangelopoulos  
<a.e.a.evangelopoulos at sms.ed.ac.uk> wrote:

> Hello all,
>
> I'm having 2 problems with solving the following ordinary differential 
> equation:
>
> h*h'[t]==-a*h^2+c
>
> Problem 1:
> Mathematica doesn't like the form of the above:
> DSolve[{h'[t]\[Equal]-a*h[t]+c/h, h[0]\[Equal]0}, h[t], t]
> returns
> DSolve::dvnoarg : The function h appears with no arguments. More...
>
> If, now, I reduce the above equation to
> DSolve[{1/2*u'[t]\[Equal]-a*u[t]+c,u[0]\[Equal]0},u[t],t]
> (by substitution of u=h^2)
> then Mathematica solves for u[t] without complaints. The thing is,  
> though, I could solve the latter by hand, really, so what's the point? 
> Is Mathematica not supposed to be able to solve the equation in the  
> first form, really (it appears to be non-linear, but intrinsically it' s  
> not)?
>
> Problem 2:
> I 'd like to impose a time dependent boundary condition, so, instead of  
> h[0]u=0, something like h[t]==v (some constant), or, the more 
> complicated, h[t]==t. How do I solve that? I have tried as follows , with  
> the reduced u[t] form:
> DSolve[{u'[t]/2\[Equal]-a*u[t]+c,u[t]\[Equal]v^2},u[t],t]
> resulting in
> DSolve::overdet : The system has fewer dependent variables than  
> equations, so is overdetermined. More...
>
> Thank you, all, for your help, in advance.
>
> Apostolos
>
>



-- 
DrMajorBob at bigfoot.com


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