ODE
\[ y'(x)=\cos (x) \sec ^2(y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0290052 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [2 \left (\frac {\text {$\#$1}}{2}+\frac {1}{4} \sin (2 \text {$\#$1})\right )\& \right ]\left [c_1+2 \sin (x)\right ]\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 18
\[ \left \{ \sin \left ( x \right ) -{\frac {\sin \left ( 2\,y \left ( x \right ) \right ) }{4}}-{\frac {y \left ( x \right ) }{2}}+{\it \_C1}=0 \right \} \] 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),'implicit')
Maple raw output
sin(x)-1/4*sin(2*y(x))-1/2*y(x)+_C1 = 0