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MathGroup Archive 1996

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Re: {mg4091] ODE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4154] Re: {mg4091] ODE
  • From: hagai at helix.nih.gov (Hagai Agmon-Snir)
  • Date: Sat, 8 Jun 1996 13:23:30 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

At 1:16 4/6/96, Robert Zimmerman wrote:
>     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*)

In[19]:=
gensol=DSolve[x y'[x]+(x+2) y[x]==2  Exp[-x],y[x],x]
Out[19]=
           -x    -x - 2 Log[x]
{{y[x] -> E   + E              C[1]}}

At x=0, y[0] is infinity or -infinity, unless C[1]=0. I suppose that
Mathematica assumes that y0 is finite (initial conditions that you write
should be finite). Then Mathematica is correct about its answer.

Hagai

>>>>>>>>>>>>>>>>>>  ================================  <<<<<<<<<<<<<<<<<
Hagai Agmon-Snir                                    Tel: (301) 496-9972
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E-mail: hagai at helix.nih.gov         WWW: http://mrb.niddk.nih.gov/hagai
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