Internal problem ID [15105]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 217.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {-y^{\prime }-\sin \left (y^{\prime }\right )=-x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(x=diff(y(x),x)+sin(diff(y(x),x)),y(x), singsol=all)
\[ y \left (x \right ) = \int \operatorname {RootOf}\left (-x +\textit {\_Z} +\sin \left (\textit {\_Z} \right )\right )d x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 38
DSolve[x==y'[x]+Sin[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=K[1]+\sin (K[1]),y(x)=\frac {K[1]^2}{2}+K[1] \sin (K[1])+\cos (K[1])+c_1\right \},\{y(x),K[1]\}\right ] \]