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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!

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    $\begingroup$ Of course, this is a bug. And a very old one. I see it in versions 5.2 and 8.0.4 of Mathematica. $\endgroup$ – innaiz Sep 25 at 17:38
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GeneratedParameters should resolve Your problem. GeneratedParameters is an option to such functions as DSolve, RSolve, and Reduce.

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    $\begingroup$ 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 $\endgroup$ – C. B. Sep 24 at 17:55
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    $\begingroup$ It is clear that the answer should be f[x,y]==f1[x]+f2[y] and g[x,y]=g1[x]+g2[y]. And certainly fi needs not be equal to gi. So, this is a bug. Please send a message to "support@wolfrom.com" $\endgroup$ – Daniel Huber Sep 24 at 18:28

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