ODE
\[ y''(x)+2 y'(x)^2 \tan (y(x))+2 \cot (x) y'(x)=0 \] ODE Classification
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.382783 (sec), leaf count = 14
\[\left \{\left \{y(x)\to \tan ^{-1}(c_1 \cot (x)+c_2)\right \}\right \}\]
Maple ✓
cpu = 0.571 (sec), leaf count = 15
\[[y \left (x \right ) = -\arctan \left (\textit {\_C1} \cot \left (x \right )-\textit {\_C2} \right )]\] Mathematica raw input
DSolve[2*Cot[x]*y'[x] + 2*Tan[y[x]]*y'[x]^2 + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ArcTan[C[2] + C[1]*Cot[x]]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)^2*tan(y(x))+2*cot(x)*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = -arctan(_C1*cot(x)-_C2)]