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


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


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