4.3.23 \(y'(x)=\tan (x) (\tan (y(x))+\sec (x) \sec (y(x)))\)

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 = 0.0938504 (sec), leaf count = 20

\[\left \{\left \{y(x)\to \sin ^{-1}\left (\frac {1}{4} \sec (x) \left (c_1-4 \log (\cos (x))\right )\right )\right \}\right \}\]

Maple
cpu = 0.929 (sec), leaf count = 18

\[ \left \{ {\frac {\sin \left (y \relax (x ) \right ) }{\sec \relax (x ) }}+\ln \left (\cos \relax (x ) \right ) -{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/sec(x)*sin(y(x))+ln(cos(x))-_C1 = 0