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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



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