# Bug in DSolve when solving a system of two second order PDEs?

I'm solving a simple system of PDEs in Mathematica 11.1:

DSolve[{D[f[x, y], x, y] == 0, D[g[x, y], x, y] == 0}, {f[x, y], g[x, y]}, {x, y}]


This gives:

{{f[x, y] -> C[1][x] + C[2][y], g[x, y] -> C[1][x] + C[2][y]}}


I expect the general solution to be:

{{f[x, y] -> C[1][x] + C[2][y], g[x, y] -> C[3][x] + C[4][y]}}


What do you think?

Thanks!

• Of course, this is a bug. And a very old one. I see it in versions 5.2 and 8.0.4 of Mathematica. – innaiz Sep 25 at 17:38

• GeneratedParameters only changes the C to the provided name... not the numbers. From the help: "is an option that specifies how parameters generated to represent the results of various symbolic operations should be named." My issue is with the numbering of the parameters: I expect 4 different parameters and not only 2 as provided by DSolve – C. B. Sep 24 at 17:55