Re: coding problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg60188] Re: coding problem*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Tue, 6 Sep 2005 05:28:51 -0400 (EDT)*Organization*: The University of Western Australia*References*: <dfj9bg$rfm$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <dfj9bg$rfm$1 at smc.vnet.net>, "Ming Hong" <zhongming at gmail.com> wrote: > I am trying to solve the following equations: > > xy''+(1+x)y'=0 > xy'(0)=-1/2 This condition does not make sense. What you mean is that as x -> 0, x y'[x] -> -1/2 > y(Infinity)=0 > > Here is what I put into Mathematica: > > Dsolve[{x*y''[x]+(1+x)*y'[x]==0,x*y'[0]==-1/2,y[Infinity]==0},y,x] > > It didn't work and I can not figure out why. Here is one way to solve your equations. First drop the problematic condition and obtain the general solution: sol = First[DSolve[{x y''[x]+(1+x) y'[x]==0, y[Infinity]==0},y,x]] Now determine the remaining constant: cond = x y'[x] == -(1/2) /. sol /. x -> 0 and obtain the desired solution: y[x] /. sol /. First[Solve[cond, C[1]]] The result is -1/2 ExpIntegralEi[-x] Cheers, Paul _______________________________________________________________________ Paul Abbott Phone: 61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul