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Re: ODE


>From: bob at zim.uoregon.edu (Robert Zimmerman)
>Subject: {mg4091] ODE
>Organization: University of Oregon

     While  lectureing with Mathematica I noticed that the following ODE   
does  not return the correct  initial conditions. 
    Is this an error or standard procedure?

 eq1=    {    x y'[x]+(x+2) y[x]==2  Exp[-x],  y[0]==y0};
 
 sol=    y[x]/.(eq1//  DSolve[#,y[x] ,x]&//Flatten)
 
 
 sol/.x->0       (*Should equal to y0 and not 1*)

Out[64]=      E^(-x)
Out[67]=        1     (*Should equal to y0 and not 1*)



The answer to your question is that x=0 is a singular point
of the ODE, and so you can not specify arbitrary initial
conditions.

I hope this helps.

Jay H. Wolkowisky

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