Simple PDE with side conditions

*To*: mathgroup at smc.vnet.net*Subject*: [mg115365] Simple PDE with side conditions*From*: "Dave Snead" <dsnead6 at charter.net>*Date*: Sun, 9 Jan 2011 02:17:43 -0500 (EST)*References*: <201101080838.DAA01905@smc.vnet.net>

Hi everybody, I'm trying to have Mathematica 7 solve a simple partial differential equation with an initial condition and a function composition condition. So my input is: In[1]:= T[f_] := D[f, t] In[2]:= X[f_] := -y*D[f, x] + x*D[f, y] In[3]:= DSolve[{ T[f[t, x, y]] == X[f[t, x, y]], f[0, x, y] == {x, y}, f[t, f[s, x, y][[1]], f[s, x, y][[2]]] == f[t + s, x, y]}, f[t, x, y], {t, x, y}] However Mathematica returns with: DSolve::conarg:The arguments should be ordered consistently Out[3]= DSolve[{Derivative[1, 0, 0][f][t, x, y] == x*Derivative[0, 0, 1][f][t, x, y] - y*Derivative[0, 1, 0][f][t, x, y], f[0, x, y] == {x, y}, f[t, s, x] == f[s + t, x, y]}, f[t, x, y], {t, x, y}] Now I know what the function f[t,x,y] is and I can verify that it satisfies my conditions: In[4]:= f[t_, x_, y_] = {x *Cos[t] - y* Sin[t], x* Sin[t] + y* Cos[t]} In[5]:= { T[f[t, x, y]] == X[f[t, x, y]], f[0, x, y] == {x, y}, f[t, f[s, x, y][[1]], f[s, x, y][[2]]] == f[t + s, x, y]} // Simplify Out[5]= {True, True, True} The question is -- how can I have Mathematica solve this problem. Thanks, Dave Snead

**References**:**Tensor cross vector***From:*solid-state <phmech@gmail.com>