ODE
\[ y'(x)^2 \sin \left (y'(x)\right )=y(x) \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 0.0484101 (sec), leaf count = 27
\[\text {Solve}\left [\left \{\cos (\text {K$\$$262683})+x=c_1+\text {K$\$$262683} \sin (\text {K$\$$262683}),\text {K$\$$262683}^2 \sin (\text {K$\$$262683})=y(x)\right \},\{y(x),\text {K$\$$262683}\}\right ]\]
Maple ✓
cpu = 0.066 (sec), leaf count = 32
\[ \left \{ x-\int ^{y \left ( x \right ) }\! \left ( {\it RootOf} \left ( \sin \left ( {\it \_Z} \right ) {{\it \_Z}}^{2}-{\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[Sin[y'[x]]*y'[x]^2 == y[x],y[x],x]
Mathematica raw output
Solve[{x + Cos[K$262683] == C[1] + K$262683*Sin[K$262683], K$262683^2*Sin[K$262683] == y[x]}, {y[x], K$262683}]
Maple raw input
dsolve(diff(y(x),x)^2*sin(diff(y(x),x)) = y(x), y(x),'implicit')
Maple raw output
y(x) = 0, x-Intat(1/RootOf(sin(_Z)*_Z^2-_a),_a = y(x))-_C1 = 0