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