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>*Reply-to*: drmajorbob at bigfoot.com

> 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[0]=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] == 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 > > -- DrMajorBob at bigfoot.com

**References**:**Problem with a 1st order IV ODE (nonlinear)***From:*Virgil Stokes <vs@it.uu.se>