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 = 0.00944599 (sec), leaf count = 0 , could not solve
DSolve[x + a*Cos[Derivative[1][y][x]] + b*Derivative[1][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.028 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) =\int \!{\it RootOf} \left ( a\cos \left ( {\it \_Z} \right ) +b{\it \_Z}+x \right ) \,{\rm d}x+{\it \_C1} \right \} \] Mathematica raw input
DSolve[x + a*Cos[y'[x]] + b*y'[x] == 0,y[x],x]
Mathematica raw output
DSolve[x + a*Cos[Derivative[1][y][x]] + b*Derivative[1][y][x] == 0, y[x], x]
Maple raw input
dsolve(a*cos(diff(y(x),x))+b*diff(y(x),x)+x = 0, y(x),'implicit')
Maple raw output
y(x) = Int(RootOf(a*cos(_Z)+b*_Z+x),x)+_C1