\[ y'(x)+2 \tan (x) \tan (y(x))-1=0 \] ✓ Mathematica : cpu = 1.58851 (sec), leaf count = 220
\[\text {Solve}\left [c_1=\frac {\frac {1}{2} \left (\frac {1}{\frac {i \tan (x)}{\tan ^2(x)+1}-\frac {i \tan ^2(x) \tan (y(x))}{\tan ^2(x)+1}}+i \cot (x)\right ) \sqrt [4]{1-\left (\frac {1}{\frac {i \tan (x)}{\tan ^2(x)+1}-\frac {i \tan ^2(x) \tan (y(x))}{\tan ^2(x)+1}}+i \cot (x)\right )^2} \, _2F_1\left (\frac {1}{2},\frac {5}{4};\frac {3}{2};\left (i \cot (x)+\frac {1}{\frac {i \tan (x)}{\tan ^2(x)+1}-\frac {i \tan ^2(x) \tan (y(x))}{\tan ^2(x)+1}}\right )^2\right )+i \tan (x)}{\sqrt [4]{-1+\left (\frac {1}{\frac {i \tan (x)}{\tan ^2(x)+1}-\frac {i \tan ^2(x) \tan (y(x))}{\tan ^2(x)+1}}+i \cot (x)\right )^2}},y(x)\right ]\] ✓ Maple : cpu = 1.573 (sec), leaf count = 78
\[c_{1}+\frac {\tan \relax (x )}{\left (\frac {\left (1+\tan ^{2}\left (y \relax (x )\right )\right ) \left (1+\tan ^{2}\relax (x )\right )}{\left (\tan \left (y \relax (x )\right ) \tan \relax (x )-1\right )^{2}}\right )^{\frac {1}{4}}}+\frac {\left (\tan \left (y \relax (x )\right )+\tan \relax (x )\right ) \hypergeom \left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (\tan \left (y \relax (x )\right )+\tan \relax (x )\right )^{2}}{\left (\tan \left (y \relax (x )\right ) \tan \relax (x )-1\right )^{2}}\right )}{2 \tan \left (y \relax (x )\right ) \tan \relax (x )-2} = 0\]