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 = 0.25775 (sec), leaf count = 29
\[\text {Solve}[\{x=\tan (K[1])+c_1,K[1] \tan (K[1])+\log (\cos (K[1]))=y(x)\},\{y(x),K[1]\}]\]
Maple ✓
cpu = 0.205 (sec), leaf count = 33
\[\left [y \left (x \right ) = 0, x -\left (\int _{}^{y \left (x \right )}\frac {1}{\RootOf \left (\ln \left (\cos \left (\textit {\_Z} \right )\right )+\textit {\_Z} \tan \left (\textit {\_Z} \right )-\textit {\_a} \right )}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] 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[1]], Log[Cos[K[1]]] + K[1]*Tan[K[1]] == y[x]}, {y[x], K[1]}]
Maple raw input
dsolve(ln(cos(diff(y(x),x)))+diff(y(x),x)*tan(diff(y(x),x)) = y(x), y(x))
Maple raw output
[y(x) = 0, x-Intat(1/RootOf(ln(cos(_Z))+_Z*tan(_Z)-_a),_a = y(x))-_C1 = 0]