ODE No. 81

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y'(x)+2 \tan (x) \tan (y(x))-1=0 \] Mathematica : cpu = 43.5407 (sec), leaf count = 0 , could not solve

DSolve[-1 + 2*Tan[x]*Tan[y[x]] + Derivative[1][y][x] == 0, y[x], x]

Maple : cpu = 1.188 (sec), leaf count = 78

\[ \left \{ {\it \_C1}+{\tan \left ( x \right ) {\frac {1}{\sqrt [4]{{\frac { \left ( 1+ \left ( \tan \left ( y \left ( x \right ) \right ) \right ) ^{2} \right ) \left ( 1+ \left ( \tan \left ( x \right ) \right ) ^{2} \right ) }{ \left ( \tan \left ( y \left ( x \right ) \right ) \tan \left ( x \right ) -1 \right ) ^{2}}}}}}}+{\frac {\tan \left ( y \left ( x \right ) \right ) +\tan \left ( x \right ) }{2\,\tan \left ( y \left ( x \right ) \right ) \tan \left ( x \right ) -2}{\mbox {$_2$F$_1$}({\frac {1}{2}},{\frac {5}{4}};\,{\frac {3}{2}};\,-{\frac { \left ( \tan \left ( y \left ( x \right ) \right ) +\tan \left ( x \right ) \right ) ^{2}}{ \left ( \tan \left ( y \left ( x \right ) \right ) \tan \left ( x \right ) -1 \right ) ^{2}}})}}=0 \right \} \]