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I am trying to solve the following partial differential equation for the function $f(x,y,z)$

$\frac{(\alpha -\beta y)}{1-y^2}\left(\frac{\partial f}{\partial x} + \frac{(\alpha y-\beta ) }{\sqrt{1-y^2}}\frac{\partial f}{\partial z} \right)-\sqrt{1-y^2} z \frac{\partial f}{\partial y}=0$

When solving with Mathematica with the following command

DSolve[-Sqrt[1 - y^2] z Derivative[0, 1, 0][f][x, y, 
     z] + ((α - 
      y β) (((y α - β) Derivative[0, 0, 1][f][x, y,
         z])/Sqrt[1 - y^2] + Derivative[1, 0, 0][f][x, y, z]))/(
   1 - y^2) == 0, f, {x, y, z}]

DSolve gives me the following error output, involving this object DsolvePDEDump`const$1049:

{{f -> Function[{x, y, z}, 
    C[1][(-z^2 + y^2 z^2 - α^2 + 
      2 y α β - β^2)/(2 (-1 + y^2)), 
     x + (1/(2 Sqrt[-(-1 + y^2)^2]))(-1 + y^2) (Log[1 - y] - 
         Log[1 + y] + 
         Log[α^2 + β^2 - 
           2 (1 + y) DSolve`DSolvePDEDump`const$1049[
             1] + β Sqrt[α^2 - 
             2 y α β + β^2 + 
             2 (-1 + y^2) DSolve`DSolvePDEDump`const$1049[
               1]] + α (β - y β + 
              Sqrt[α^2 - 2 y α β + β^2 + 
               2 (-1 + y^2) DSolve`DSolvePDEDump`const$1049[1]])] - 
         Log[α^2 + β^2 + 
           2 (-1 + y) DSolve`DSolvePDEDump`const$1049[
             1] - β Sqrt[α^2 - 
             2 y α β + β^2 + 
             2 (-1 + y^2) DSolve`DSolvePDEDump`const$1049[
               1]] + α (-(1 + y) β + 
              Sqrt[α^2 - 2 y α β + β^2 + 
               2 (-1 + y^2) DSolve`DSolvePDEDump`const$1049[1]])])]]}}

A similar problem has been discussed here DSolve giving strange error messages solving a PDE . An answer claims that the bug has been resolved in Mathematica 10.1.0, but I am getting this error with version 10.2.0.

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  • 1
    $\begingroup$ Same error occurs for "10.3.0 for Microsoft Windows (64-bit) (October 9, 2015)" $\endgroup$ – bbgodfrey Dec 4 '15 at 2:14
  • 1
    $\begingroup$ In Mathematica 10.4.0, it returns unevaluated $\endgroup$ – user58955 Mar 26 '16 at 4:21

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