ODE
\[ y'(x)=\cos (x) \sec ^2(y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.248313 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [2 \left (\frac {\text {$\#$1}}{2}+\frac {1}{4} \sin (2 \text {$\#$1})\right )\& \right ][2 \sin (x)+c_1]\right \}\right \}\]
Maple ✓
cpu = 0.112 (sec), leaf count = 22
\[\left [y \left (x \right ) = \frac {\RootOf \left (-\textit {\_Z} +4 \textit {\_C1} +4 \sin \left (x \right )-\sin \left (\textit {\_Z} \right )\right )}{2}\right ]\] Mathematica raw input
DSolve[y'[x] == Cos[x]*Sec[y[x]]^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[2*(Sin[2*#1]/4 + #1/2) & ][C[1] + 2*Sin[x]]}}
Maple raw input
dsolve(diff(y(x),x) = cos(x)*sec(y(x))^2, y(x))
Maple raw output
[y(x) = 1/2*RootOf(-_Z+4*_C1+4*sin(x)-sin(_Z))]