4.3.10 \(y'(x)=\sec ^2(x) \text {Cosy}(y(x)) \cot (y(x))\)

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 = 0.427983 (sec), leaf count = 28

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {\tan (K[1])}{\text {Cosy}(K[1])} \, dK[1]\& \right ]\left [c_1+\tan (x)\right ]\right \}\right \}\]

Maple
cpu = 0.049 (sec), leaf count = 33

\[ \left \{ {\frac {1}{\cos \relax (x ) } \left (-\int ^{y \relax (x ) }\!{\frac {1}{\cot \left ({\it \_a} \right ) {\it Cosy} \left ({\it \_a} \right ) }}{d{\it \_a}}\cos \relax (x ) +{\it \_C1}\,\cos \relax (x ) +\sin \relax (x ) \right ) }=0 \right \} \] Mathematica raw input

DSolve[y'[x] == Cosy[y[x]]*Cot[y[x]]*Sec[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> InverseFunction[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),'implicit')

Maple raw output

(-Intat(1/cot(_a)/Cosy(_a),_a = y(x))*cos(x)+_C1*cos(x)+sin(x))/cos(x) = 0