ODE
\[ y'(x)+\sin \left (y'(x)\right )=x \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(x\)
Mathematica ✓
cpu = 0.190181 (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 = 0.187 (sec), leaf count = 16
\[[y \left (x \right ) = \int \RootOf \left (\sin \left (\textit {\_Z} \right )+\textit {\_Z} -x \right )d x +\textit {\_C1}]\] Mathematica raw input
DSolve[Sin[y'[x]] + y'[x] == x,y[x],x]
Mathematica raw output
Solve[{x == K[1] + Sin[K[1]], y[x] == C[1] + Cos[K[1]] + K[1]^2/2 + K[1]*Sin[K[1]]}, {y[x], K[1]}]
Maple raw input
dsolve(sin(diff(y(x),x))+diff(y(x),x) = x, y(x))
Maple raw output
[y(x) = Int(RootOf(sin(_Z)+_Z-x),x)+_C1]