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
>
>
>
>