Internal problem ID [8148]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 568.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2} \sin \left (y^{\prime }\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 32
dsolve(diff(y(x),x)^2*sin(diff(y(x),x))-y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ x -\left (\int _{}^{y \relax (x )}\frac {1}{\RootOf \left (\sin \left (\textit {\_Z} \right ) \textit {\_Z}^{2}-\textit {\_a} \right )}d \textit {\_a} \right )-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 34
DSolve[-y[x] + Sin[y'[x]]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=K[1] \sin (K[1])-\cos (K[1])+c_1,y(x)=K[1]^2 \sin (K[1])\right \},\{y(x),K[1]\}\right ] \]