ODE
\[ y'(x)=\tan (x) (\tan (y(x))+\sec (x) \sec (y(x))) \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.448042 (sec), leaf count = 20
\[\left \{\left \{y(x)\to \sin ^{-1}\left (\frac {1}{4} \sec (x) (-4 \log (\cos (x))+c_1)\right )\right \}\right \}\]
Maple ✓
cpu = 1.043 (sec), leaf count = 17
\[[y \left (x \right ) = \arcsin \left (-\ln \left (\cos \left (x \right )\right ) \sec \left (x \right )+\textit {\_C1} \sec \left (x \right )\right )]\] Mathematica raw input
DSolve[y'[x] == Tan[x]*(Sec[x]*Sec[y[x]] + Tan[y[x]]),y[x],x]
Mathematica raw output
{{y[x] -> ArcSin[((C[1] - 4*Log[Cos[x]])*Sec[x])/4]}}
Maple raw input
dsolve(diff(y(x),x) = tan(x)*(tan(y(x))+sec(x)*sec(y(x))), y(x))
Maple raw output
[y(x) = arcsin(-ln(cos(x))*sec(x)+_C1*sec(x))]