User tony - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T20:05:24Z http://mathoverflow.net/feeds/user/29214 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/113776/coupled-first-order-pdes-in-two-unknowns Coupled first order pdes in two unknowns Tony 2012-11-18T22:14:52Z 2012-11-19T09:18:35Z <p>Hello,</p> <p>I have what appears at first sight to be a simple system of coupled first order pdes in two unknowns which I need to solve simultaenously:</p> <p>$\frac{\partial f(x,y)}{\partial x}=(x+y)*x*f(x,y) \quad;\quad \frac{\partial f(x,y)}{\partial y}=(x+y)*y*f(x,y)$</p> <p>But there doesnt seem to be a solution that I or mathematica can come up with. Does anyone have a suggestion for a solution. Or conversely a proof that it has no solution?</p> http://mathoverflow.net/questions/113776/coupled-first-order-pdes-in-two-unknowns/113810#113810 Comment by Tony Tony 2012-11-19T10:28:20Z 2012-11-19T10:28:20Z thanks, thats a really fruitful way of looking at it. I knew I had to ask a mathematician :)