Re: Please help me to solve a PDE's system
- To: mathgroup at smc.vnet.net
- Subject: [mg42177] Re: [mg42151] Please help me to solve a PDE's system
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sat, 21 Jun 2003 20:56:57 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Saturday, June 21, 2003, at 03:49 PM, Ciuca Marian George wrote:
>
> I want to find u:R^2->R which is the solution of the following
> system:
>
> D[u[x,y],x] = 2 x
>
> D[u[x,y],y] = 2 y
>
> It is very easy to see that the solution, in this case is
> u(x,y)=x^2 + y^2 + k,
> where k is a real constant.
>
> Generally speaking, i have a more important system to solve but even
> for
> this system i could not find the solution using Mathematica.
>
> Thank you in advance,
> George.
>
>
>
>
How about something like this:
Block[{g, h},
First[g /. DSolve[
D[g = f[x, y] /. DSolve[{D[f[x, y], x] == 2*x},
f[x, y], {x, y}][[1]] /. C[1] -> h, y] == 2*y,
h[y], y]]]
x^2 + y^2 + C[1]
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/