Problem with a 1st order IV ODE (nonlinear)

*To*: mathgroup at smc.vnet.net*Subject*: [mg102564] Problem with a 1st order IV ODE (nonlinear)*From*: Virgil Stokes <vs at it.uu.se>*Date*: Fri, 14 Aug 2009 05:59:03 -0400 (EDT)

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] == 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] == 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

**Follow-Ups**:**Re: Re: Problem with a 1st order IV ODE***From:*Leonid Shifrin <lshifr@gmail.com>

**Re: Problem with a 1st order IV ODE (nonlinear)***From:*Leonid Shifrin <lshifr@gmail.com>

**Re: Problem with a 1st order IV ODE (nonlinear)***From:*danl@wolfram.com

**Re: Problem with a 1st order IV ODE (nonlinear)***From:*DrMajorBob <btreat1@austin.rr.com>