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

• To: mathgroup at smc.vnet.net
• Subject: [mg102583] Re: Problem with a 1st order IV ODE (nonlinear)
• From: Harutyun <amirjanyan at gmail.com>
• Date: Sat, 15 Aug 2009 05:34:25 -0400 (EDT)
• References: <h63ch5$1bu$1@smc.vnet.net>

you are getting analytic solution due to fortunate choice of parameters
R =.;
k = 1/R^2;
sol = DSolve[{h'[t] == 1/(h[t] (2 R - h[t])) - k, h[0] == 0}, h[t],
   t] // FullSimplify
for which
{{h[t] -> -((t + Sqrt[t (4 R^3 + t)])/(2 R^2))}, {h[t] -> (-t + Sqrt[
    t (4 R^3 + t)])/(2 R^2)}}
in general case
DSolve[h'[t] == 1/(h[t] (2 R - h[t])) - k, h[t],  t]
will get expression with InverseFunction
which cannot be solved analytically