Internal problem ID [8146]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 566.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\sin \left (y^{\prime }\right )+y^{\prime }-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(sin(diff(y(x),x))+diff(y(x),x)-x=0,y(x), singsol=all)
\[ y \relax (x ) = \int \RootOf \left (\sin \left (\textit {\_Z} \right )+\textit {\_Z} -x \right )d x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 38
DSolve[-x + Sin[y'[x]] + y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=K[1]+\sin (K[1]),y(x)=\frac {K[1]^2}{2}+K[1] \sin (K[1])+\cos (K[1])+c_1\right \},\{y(x),K[1]\}\right ] \]