ODE
\[ y'(x) \sin \left (y'(x)\right )+\cos \left (y'(x)\right )=y(x) \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 0.205851 (sec), leaf count = 28
\[\text {Solve}[\{x=\sin (K[1])+c_1,K[1] \sin (K[1])+\cos (K[1])=y(x)\},\{y(x),K[1]\}]\]
Maple ✓
cpu = 2.451 (sec), leaf count = 32
\[\left [y \left (x \right ) = 1, x -\left (\int _{}^{y \left (x \right )}\frac {1}{\RootOf \left (\textit {\_Z} \sin \left (\textit {\_Z} \right )+\cos \left (\textit {\_Z} \right )-\textit {\_a} \right )}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[Cos[y'[x]] + Sin[y'[x]]*y'[x] == y[x],y[x],x]
Mathematica raw output
Solve[{x == C[1] + Sin[K[1]], Cos[K[1]] + K[1]*Sin[K[1]] == y[x]}, {y[x], K[1]}]
Maple raw input
dsolve(diff(y(x),x)*sin(diff(y(x),x))+cos(diff(y(x),x)) = y(x), y(x))
Maple raw output
[y(x) = 1, x-Intat(1/RootOf(_Z*sin(_Z)+cos(_Z)-_a),_a = y(x))-_C1 = 0]