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 Graduate Student UMBC Department of Mechanical Engineering Phone: 410 455 8134

**References**:**Partial diff equations***From:*David Boily <dsboily@fastmail.ca>