Solving differential equations in the complex plane

*To*: mathgroup at smc.vnet.net*Subject*: [mg103768] Solving differential equations in the complex plane*From*: Andre Hautot <ahautot at ulg.ac.be>*Date*: Mon, 5 Oct 2009 07:39:48 -0400 (EDT)

Hi ! How can I solve an ordinary differential equation of order n in the complex plane following a prescribed contour ? I can of course write my own Runge-Kutta package but is there a quickest way to do that (maybe NDSolve but how to define the contour ??) ? Example : NDSolve[{y'[x] == Exp[y[x]], y[1] == 1}, y, {x, 1, 3}] fails because of a singularity in x=1+1/e. However integrating the ODE following a path which avoids the singularity should be possible eventually leading to a multivalued function. Thanks for a hint.

**Follow-Ups**:**Re: Re: Solving differential equations in the***From:*DrMajorBob <btreat1@austin.rr.com>

**Re: Solving differential equations in the complex plane***From:*Dan Dubin <ddubin@ucsd.edu>