Re: DSolve bug

*To*: mathgroup at smc.vnet.net*Subject*: [mg97820] Re: [mg97768] DSolve bug*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Sun, 22 Mar 2009 05:50:41 -0500 (EST)*References*: <612696379.19321237704569790.JavaMail.root@mmm.inp.demokritos.gr>*Reply-to*: drmajorbob at bigfoot.com

More to the point, using Bob's example: Clear[f] f[a_][x_] := Sin[a*x] D[f[x][y], x, y] - D[f[x][y], y, x] 0 As you can see, both derivatives ARE the same. Here's a better test, I think (since a and x were used symmetrically, above): Clear[f] f[a_][x_] := Sin[a]^x diff = D[f[x][y], x, y] - D[f[x][y], y, x] 0 But let's try it Sotirios' way, keeping f symbolic for a bit: Clear[f] raw=D[f[x][y],x,y]-D[f[x][y],y,x]; Block[{g},g[a_][x_]:=Sin[a]^x;raw/.f->g]//ExpandAll//Simplify -(Log[Sin[x]]^2 Sin[x]^#1& (g^\[Prime])[x])[y]+(g^\[Prime]\[Prime])[x][y] Now Mathematica can't equate the two derivatives. But that's a problem with D, not with DSolve. Note that Dt does better, too: Clear[f] raw = Dt[f[x][y], x, y] - Dt[f[x][y], y, x] 0 DSolve's solution IS correct. It's D that may not be all it should be. Bobby On Sun, 22 Mar 2009 01:49:29 -0500, Sotirios Bonanos <sbonano at inp.demokritos.gr> wrote: > > > 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[1][z][x] + C[2][z][y]}} >> > instead of {{F[x, y, z] -> C[1][x, z] + C[2][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/ -- DrMajorBob at bigfoot.com