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How can I get solution of this differential equation in form of tanh (not tan)

DSolve[{x - x f[x, y]^2 == Exp[ y ] D[( f[x, y] /Exp[y]), y]}, f[x, y], {x, y}]
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    $\begingroup$ DSolve[{x - x f[x, y]^2 == Exp[y] D[(f[x, y]/Exp[y]), y]}, f[x, y], {x, y}] /. Sqrt[x_] :> I Sqrt[-x] /. Tan[x_] :> Tan@Expand@x. $\endgroup$ – march Sep 29 '17 at 21:13
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DSolve[{x - x f[x, y]^2 == Exp[y] D[(f[x, y]/Exp[y]), y]}, 
  f[x, y], {x, y}];

Assuming[-(1/2) < x < 1/2, FullSimplify[%]]
(* {{f[x, y] -> (
   1 - Sqrt[1 + 4 x^2] Tanh[1/2 Sqrt[1 + 4 x^2] (-y + C[1][x])])/(
   2 x)}} *)
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