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 = 0.250772 (sec), leaf count = 33
\[\text {Solve}\left [\left \{\cos (K[1])+x=K[1] \sin (K[1])+c_1,K[1]^2 \sin (K[1])=y(x)\right \},\{y(x),K[1]\}\right ]\]
Maple ✓
cpu = 0.508 (sec), leaf count = 32
\[\left [y \left (x \right ) = 0, x -\left (\int _{}^{y \left (x \right )}\frac {1}{\RootOf \left (\sin \left (\textit {\_Z} \right ) \textit {\_Z}^{2}-\textit {\_a} \right )}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[Sin[y'[x]]*y'[x]^2 == y[x],y[x],x]
Mathematica raw output
Solve[{x + Cos[K[1]] == C[1] + K[1]*Sin[K[1]], K[1]^2*Sin[K[1]] == y[x]}, {y[x], K[1]}]
Maple raw input
dsolve(diff(y(x),x)^2*sin(diff(y(x),x)) = y(x), y(x))
Maple raw output
[y(x) = 0, x-Intat(1/RootOf(sin(_Z)*_Z^2-_a),_a = y(x))-_C1 = 0]