       Re: Problem with a 1st order IV ODE (nonlinear)

• To: mathgroup at smc.vnet.net
• Subject: [mg102584] Re: [mg102564] Problem with a 1st order IV ODE (nonlinear)
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Sat, 15 Aug 2009 05:34:36 -0400 (EDT)
• References: <200908140959.FAA01407@smc.vnet.net>

```> Is there anyway that I can get an analytical solution to this problem
> for these conditions?

Absolutely not. With that boundary condition, which makes the derivative
undefined at 0? No way.

However, substituting h=1 doesn't get us any farther, so I'll be
curious to see answers from more expert mathematicians.

Bobby

On Fri, 14 Aug 2009 04:59:03 -0500, Virgil Stokes <vs at it.uu.se> wrote:

> I am using Mathematica 7.0 on a Win2K platform and noticed that when I
> execute the following:
>
> R = 10;
> k = 0.01;
> sol = DSolve[{h'[t] == 1/(h[t] (2 R - h[t])) - k, h == 0}, h[t], t]
> // FullSimplify
>
> I get two possible solutions:
> {{h[t] -> -0.005 t - 0.005 Sqrt[t (4000. + t)]}, {h[t] -> -0.005 t +
> 0.005 Sqrt[t (4000. + t)]}}
>
> which, I believe are correct. However, if I try to get an analytical
> solution in terms of R and k,
>
> Clear[R, k]
> sol = DSolve[{h'[t] == 1/(h[t] (2 R - h[t])) - k, h == 0}, h[t],  t]
> // FullSimplify
>
> I get the following two output messages:
> Solve::tdep: The equations appear to involve the variables to be solved
> for in an essentially non-algebraic way.
> DSolve::bvnul: For some branches of the general solution, the given
> boundary conditions lead to an empty solution.
>
> Note, that R > 0, and  k >= 0..
> Is there anyway that I can get an analytical solution to this problem
> for these conditions?
>
> --V. Stokes
>
>

--
DrMajorBob at bigfoot.com

```

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