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MathGroup Archive 2002

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Re: Peculiar output from DSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36997] Re: [mg36994] Peculiar output from DSolve
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sun, 6 Oct 2002 05:32:31 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

It isn't so. C[1] is an arbitrary (smooth) function. After all, what 
you have got is a partial differential equation. For example, you can 
take C[1] to be Sin:

In[1]:=
v[x_, y_] = u[x, y] /. DSolve[y*D[u[x, y], x] ==
       x*D[u[x, y], y], u[x, y], {x, y}] /. C[1] -> Sin

Out[1]=
{Sin[(1/2)*(x^2 + y^2)]}

In[2]:=
y*D[v[x, y], x] == x*D[v[x, y], y]

Out[2]=
True

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/


On Friday, October 4, 2002, at 06:01 PM, Selwyn Hollis wrote:

>
> In:  DSolve[y*D[u[x, y],x] == x*D[u[x, y],y], u[x,y], {x, y}]
>
> Out:  {{u[x, y] -> C[1][(1/2)*(x^2 + y^2)]}}
>
> Square brackets are used as grouping symbols in the result!??  :^O
>
> Somebody say it isn't so.
>
> ---
> Selwyn Hollis
>
>
>
>



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