ODE No. 81

$$y^{\prime }(x)+2\tan (x)\tan (y(x))-1=0$$ ✓ Mathematica : cpu = 1.58851 (sec), leaf count = 220

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

$$\text{Solve}[c_1=\frac{\frac{1}{2}(\frac{1}{\frac{i\tan (x)}{{\tan }^2(x)+1}-\frac{i{\tan }^2(x)\tan (y(x))}{{\tan }^2(x)+1}}+i\cot (x))\sqrt[4]{1-{(\frac{1}{\frac{i\tan (x)}{{\tan }^2(x)+1}-\frac{i{\tan }^2(x)\tan (y(x))}{{\tan }^2(x)+1}}+i\cot (x))}^2}{}_2{F}_1(\frac{1}{2},\frac{5}{4};\frac{3}{2};{(i\cot (x)+\frac{1}{\frac{i\tan (x)}{{\tan }^2(x)+1}-\frac{i{\tan }^2(x)\tan (y(x))}{{\tan }^2(x)+1}})}^2)+i\tan (x)}{\sqrt[4]{-1+{(\frac{1}{\frac{i\tan (x)}{{\tan }^2(x)+1}-\frac{i{\tan }^2(x)\tan (y(x))}{{\tan }^2(x)+1}}+i\cot (x))}^2}},y(x)]$$ ✓ Maple : cpu = 1.573 (sec), leaf count = 78

dsolve(diff(y(x),x)+2*tan(y(x))*tan(x)-1 = 0,y(x))
 

$$c_1+\frac{\tan \left(x\right)}{{\left(\frac{(1+{\tan }^2\left(y\left(x\right)\right))(1+{\tan }^2\left(x\right))}{{(\tan \left(y\left(x\right)\right)\tan \left(x\right)-1)}^2}\right)}^{\frac{1}{4}}}+\frac{(\tan \left(y\left(x\right)\right)+\tan \left(x\right))\mathrm{hypergeom}([\frac{1}{2},\frac{5}{4}],\left[\frac{3}{2}\right],-\frac{{(\tan \left(y\left(x\right)\right)+\tan \left(x\right))}^2}{{(\tan \left(y\left(x\right)\right)\tan \left(x\right)-1)}^2})}{2\tan \left(y\left(x\right)\right)\tan \left(x\right)-2}=0$$