       Re: DSolve bug

• To: mathgroup at smc.vnet.net
• Subject: [mg97819] Re: [mg97768] DSolve bug
• From: Sotirios Bonanos <sbonano at inp.demokritos.gr>
• Date: Sun, 22 Mar 2009 05:50:29 -0500 (EST)

```Your example gives two different ways of referring to the same function (Sin[a*x]). But I want to be able to use the arbitrary function in the solution given by DSolve (and its derivatives) in other expressions. This I cannot do because the derivatives D[f1[x][y], x, y], D[f1[x][y], y, x] are not equal:

Clear[f1, f2]

{D[f1[x][y], x, y], D[f1[x][y], y, x]}

That's why I claim, if it is not a bug, it is an unfortunate choice of representation!

Sotirios Bonanos

----- "Bob Hanlon" wrote:
> It is just an alternate representation
>
> Clear[f1, f2]
>
> f1[a_][x_] := Sin[a*x]
>
> f2[a_, x_] := Sin[a*x]
>
> f1[c][t] == f2[c, t]
>
> True
>
> {Plot3D[f1[a][x], {x, 0, 2 Pi}, {a, 1, 3}],
> Plot3D[f2[a, x], {x, 0, 2 Pi}, {a, 1, 3}]}
>
> Some people prefer the f[a][x] representation to explicitly separate out
> parameter(s) from argument(s)
>
> If you prefer
>
> DSolve[D[F[x, y, z], x, y] == 0, F[x, y, z], {x, y, z}]
>
> {{F(x,y,z)->Subscript[c, 1][z][x]+Subscript[c, 2][z][y]}}
>
> % /. f_[arg1_][arg2_] :> f[arg2, arg1]
>
> {{F(x,y,z)->Subscript[c, 1][x,z]+Subscript[c, 2][y,z]}}
>
>
>
> Bob Hanlon
>
>
> On Sat, Mar 21, 2009 at 10:25 AM , Sotirios Bonanos wrote:
>
> > Hello,
> > I have encountered the following bug in DSolve:
> > DSolve[D[F[x, y, z], x, y] == 0, F[x, y, z], {x, y, z}]
> > gives {{F[x, y, z] -> C[z][x] + C[z][y]}}
> > instead of {{F[x, y, z] -> C[x, z] + C[y, z]}}
> > I don't know if this has been fixed in Mathematica 7, but it is
> > present in versions 5 and 6.
> > S. Bonanos http://www.inp.demokritos.gr/~sbonano/
>

```

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