Why doesn't DSolve find all the solutions of this pde

*To*: mathgroup at smc.vnet.net*Subject*: [mg72459] Why doesn't DSolve find all the solutions of this pde*From*: "Valeri Astanoff" <astanoff at gmail.com>*Date*: Fri, 29 Dec 2006 05:11:46 -0500 (EST)

Good day, I wonder why DSolve doesn't find all the solutions of this pde : In[1]:=eq = r D[f[r,th],r] - Tan[2th] D[f[r,th],th] == 0; In[2]:=DSolve[eq ,f[r,th],{r,th}] >From In[2]:= Solve::ifun Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. Out[2]={{f[r, th] -> C[1][Log[(-r)*Sqrt[Sin[2*th]]]]}, {f[r, th] -> C[1][Log[r*Sqrt[Sin[2*th]]]]}} In[3]:=g[r_,th_] = r^2*Sin[2th]; In[4]:=eq/.f -> g Out[4]=True In[5]:=$Version Out[5]=5.1 for Microsoft Windows (January 28, 2005) With my early thanks for any advice V.Astanoff

**Follow-Ups**:**Re: Why doesn't DSolve find all the solutions of this pde***From:*Devendra Kapadia <dkapadia@wolfram.com>