\[ y'(x)+2 \tan (x) \tan (y(x))-1=0 \] ✓ Mathematica : cpu = 1.20226 (sec), leaf count = 220
DSolve[-1 + 2*Tan[x]*Tan[y[x]] + Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [c_1=\frac {\frac {1}{2} \left (\frac {1}{\frac {i \tan (x)}{\tan ^2(x)+1}-\frac {i \tan ^2(x) \tan (y(x))}{\tan ^2(x)+1}}+i \cot (x)\right ) \sqrt [4]{1-\left (\frac {1}{\frac {i \tan (x)}{\tan ^2(x)+1}-\frac {i \tan ^2(x) \tan (y(x))}{\tan ^2(x)+1}}+i \cot (x)\right )^2} \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {5}{4},\frac {3}{2},\left (i \cot (x)+\frac {1}{\frac {i \tan (x)}{\tan ^2(x)+1}-\frac {i \tan ^2(x) \tan (y(x))}{\tan ^2(x)+1}}\right )^2\right )+i \tan (x)}{\sqrt [4]{-1+\left (\frac {1}{\frac {i \tan (x)}{\tan ^2(x)+1}-\frac {i \tan ^2(x) \tan (y(x))}{\tan ^2(x)+1}}+i \cot (x)\right )^2}},y(x)\right ]\] ✓ Maple : cpu = 1.052 (sec), leaf count = 78
dsolve(diff(y(x),x)+2*tan(y(x))*tan(x)-1 = 0,y(x))
\[c_{1}+\frac {\tan \left (x \right )}{{\left (\frac {\left (1+\tan \left (y \left (x \right )\right )^{2}\right ) \left (1+\tan \left (x \right )^{2}\right )}{\left (\tan \left (y \left (x \right )\right ) \tan \left (x \right )-1\right )^{2}}\right )}^{\frac {1}{4}}}+\frac {\left (\tan \left (y \left (x \right )\right )+\tan \left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (\tan \left (y \left (x \right )\right )+\tan \left (x \right )\right )^{2}}{\left (\tan \left (y \left (x \right )\right ) \tan \left (x \right )-1\right )^{2}}\right )}{2 \tan \left (y \left (x \right )\right ) \tan \left (x \right )-2} = 0\]