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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
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