ODE
\[ y'(x)=\sec ^2(x) \text {Cosy}(y(x)) \cot (y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.522428 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\tan (K[1])}{\text {Cosy}(K[1])}dK[1]\& \right ][\tan (x)+c_1]\right \}\right \}\]
Maple ✓
cpu = 0.076 (sec), leaf count = 23
\[\left [\tan \left (x \right )-\left (\int _{}^{y \left (x \right )}\frac {1}{\cot \left (\textit {\_a} \right ) \mathit {Cosy} \left (\textit {\_a} \right )}d \textit {\_a} \right )+\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[y'[x] == Cosy[y[x]]*Cot[y[x]]*Sec[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][Tan[K[1]]/Cosy[K[1]], {K[1], 1, #1}] & ][C[1] + Tan[x]]}}
Maple raw input
dsolve(diff(y(x),x) = sec(x)^2*cot(y(x))*Cosy(y(x)), y(x))
Maple raw output
[tan(x)-Intat(1/cot(_a)/Cosy(_a),_a = y(x))+_C1 = 0]