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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: [mg78037] Re: Simple ODE with time-dep BC
  • From: dh <dh at metrohm.ch>
  • Date: Thu, 21 Jun 2007 05:59:58 -0400 (EDT)
  • References: <f5as8d$9kj$1@smc.vnet.net>


Hi Apostolos,

you are foolling yourself a bit. See below:

hope this helps, Daniel



Apostolos E. A. S. Evangelopoulos 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...

Mathematica is right, you forgot to put in the argument in: c/h

> 

> 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]==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...

PDE have boundary conditions, not ODE. by specifying h[t]=constant you 

actually give a solution that is in most cases incompatible with your 

equation.

> 

> Thank you, all, for your help, in advance.

> 

> Apostolos

> 




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