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 = 0.0299593 (sec), leaf count = 23
\[\text {Solve}\left [\left \{x=c_1+\sin (\text {K$\$$262546}),\text {K$\$$262546} \sin (\text {K$\$$262546})+\cos (\text {K$\$$262546})=y(x)\right \},\{y(x),\text {K$\$$262546}\}\right ]\]
Maple ✓
cpu = 0.063 (sec), leaf count = 32
\[ \left \{ x-\int ^{y \left ( x \right ) }\! \left ( {\it RootOf} \left ( \sin \left ( {\it \_Z} \right ) {\it \_Z}+\cos \left ( {\it \_Z} \right ) -{\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =1 \right \} \] 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$262546], Cos[K$262546] + K$262546*Sin[K$262546] == y[x]}, {y[x], K$262546}]
Maple raw input
dsolve(diff(y(x),x)*sin(diff(y(x),x))+cos(diff(y(x),x)) = y(x), y(x),'implicit')
Maple raw output
y(x) = 1, x-Intat(1/RootOf(sin(_Z)*_Z+cos(_Z)-_a),_a = y(x))-_C1 = 0