Re: Partial diff equations

• To: mathgroup at smc.vnet.net
• Subject: [mg58537] Re: [mg58510] Partial diff equations
• From: Pratik Desai <pdesai1 at umbc.edu>
• Date: Wed, 6 Jul 2005 03:11:22 -0400 (EDT)
• References: <200507050557.BAA29453@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```David Boily wrote:

>I have a not difficult to integrate but huge system of partial
>differential equations that I would never attempt to solve by hand. So I
>tried to feed it to mathematica and got the message bellow. I got annoyed and
>tested DSolve with a trivial problem only to realize that, apparently,
>mathematica is not very good when it comes to partial diff equations.
>
>Indeed, how come mathematica can't solve this simple system:
>
>DSolve[{D[f[x,y],x]==2 x y^2, D[f[x,y],y]==2 x^2 y}, f[x,y], {x, y}]
>
>the solution is trivial (f[x,y]=x^2 y^2), but if I enter the above
>command I get:
>
>DSolve::overdet:
>   The system has fewer dependent variables than equations, so is
>    overdetermined.
>
>any info would be appreciated,
>
>Thanks,
>
>David Boily
>Centre for Intelligent Machines
>McGill University
>Montreal, Quebec
>
>
>
I am not sure exactly what system you refer to in your expression, but
if you try this
sol1 = DSolve[D[f[x, y], x] == 2 x y^2, f[x, y], {x, y}] // First;
sol2 = DSolve[D[f[x, y], y] == 2 x^2 y, f[x, y], {x, y}] // First;
f1[x_, y_] = f[x, y] /. sol1
f2[x_, y_] = f[x, y] /. sol2
>>\!\(x\^2\ y\^2 + \(C[1]\)[y]\)
>>\!\(x\^2\ y\^2 + \(C[1]\)[x]\)

D[f1[x, y], x]
D[f2[x, y], y]
>>2xy^2
>>2x^2y
It seems to work fine

Best regards
Pratik

--
Pratik Desai