differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg4766] differential equation
• From: Ralph Gensheimer <ralphg at spock.physik.uni-konstanz.de>
• Date: Fri, 13 Sep 1996 13:54:50 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```dear group,

i have the folowing problem:

in an ordinary differential equation system,
(solution functions are  y1(r), y2(r), y3(r) ) is an integration in another variable x.
and in this integral there is also the solution function y3(r).
r and x are independent.
the problem has the following structure:

NDSolve[{y1'[r] == y2[r],
y2'[r] == -(2/r)*y2[r]+
(-y1[r])^(3/2)*NIntegrate[x^(1/2)/(Exp[x+y3[r]]-1),{x,0,Infinity}],
y1[r]*y3'[r] == y2[r],
y1[0.001]==-1000,
y2[0.001]==0,
y3[0.001]==0 },{y1,y2,y3},{r,0.001,0.2}]

can you give me ideas to solve this problem ?

ralph

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