ODE
\[ a \cos \left (y'(x)\right )+b y'(x)+x=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(x\)
Mathematica ✓
cpu = 0.222217 (sec), leaf count = 48
\[\text {Solve}\left [\left \{a K[1] \cos (K[1])+\frac {1}{2} b K[1]^2+y(x)=a \sin (K[1])+c_1,a \cos (K[1])+b K[1]+x=0\right \},\{y(x),K[1]\}\right ]\]
Maple ✓
cpu = 0.483 (sec), leaf count = 18
\[[y \left (x \right ) = \int \RootOf \left (a \cos \left (\textit {\_Z} \right )+\textit {\_Z} b +x \right )d x +\textit {\_C1}]\] Mathematica raw input
DSolve[x + a*Cos[y'[x]] + b*y'[x] == 0,y[x],x]
Mathematica raw output
Solve[{a*Cos[K[1]]*K[1] + (b*K[1]^2)/2 + y[x] == C[1] + a*Sin[K[1]], x + a*Cos[K[1]] + b*K[1] == 0}, {y[x], K[1]}]
Maple raw input
dsolve(a*cos(diff(y(x),x))+b*diff(y(x),x)+x = 0, y(x))
Maple raw output
[y(x) = Int(RootOf(a*cos(_Z)+_Z*b+x),x)+_C1]