2.566   ODE No. 566

\[ y'(x)+\sin \left (y'(x)\right )-x=0 \] Mathematica : cpu = 0.0404544 (sec), leaf count = 38


\[\text {Solve}\left [\left \{x=K[1]+\sin (K[1]),y(x)=\frac {K[1]^2}{2}+K[1] \sin (K[1])+\cos (K[1])+c_1\right \},\{y(x),K[1]\}\right ]\] Maple : cpu = 0.043 (sec), leaf count = 16


\[y \relax (x ) = \int \RootOf \left (\sin \left (\textit {\_Z} \right )+\textit {\_Z} -x \right )d x +c_{1}\]