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
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