ODE
\[ y'(x) \tan \left (y'(x)\right )+\log \left (\cos \left (y'(x)\right )\right )=y(x) \] ODE Classification
[_dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 0.0666211 (sec), leaf count = 24
\[\text {Solve}\left [\left \{x=c_1+\tan (\text {K$\$$267289}),\text {K$\$$267289} \tan (\text {K$\$$267289})+\log (\cos (\text {K$\$$267289}))=y(x)\right \},\{y(x),\text {K$\$$267289}\}\right ]\]
Maple ✓
cpu = 0.082 (sec), leaf count = 33
\[ \left \{ x-\int ^{y \left ( x \right ) }\! \left ( {\it RootOf} \left ( \ln \left ( \cos \left ( {\it \_Z} \right ) \right ) +{\it \_Z}\,\tan \left ( {\it \_Z} \right ) -{\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[Log[Cos[y'[x]]] + Tan[y'[x]]*y'[x] == y[x],y[x],x]
Mathematica raw output
Solve[{x == C[1] + Tan[K$267289], Log[Cos[K$267289]] + K$267289*Tan[K$267289] == y[x]}, {y[x], K$267289}]
Maple raw input
dsolve(ln(cos(diff(y(x),x)))+diff(y(x),x)*tan(diff(y(x),x)) = y(x), y(x),'implicit')
Maple raw output
y(x) = 0, x-Intat(1/RootOf(ln(cos(_Z))+_Z*tan(_Z)-_a),_a = y(x))-_C1 = 0