2.567   ODE No. 567

\[ a \cos \left (y'(x)\right )+b y'(x)+x=0 \]

✓ Mathematica : cpu = 0.0655936 (sec), leaf count = 49

DSolve[x + a*Cos[Derivative[1][y][x]] + b*Derivative[1][y][x] == 0,y[x],x]
 

\[\text {Solve}\left [\left \{y(x)=a \sin (K[1])-a K[1] \cos (K[1])-\frac {1}{2} b K[1]^2+c_1,x=-a \cos (K[1])-b K[1]\right \},\{y(x),K[1]\}\right ]\]

✓ Maple : cpu = 0.039 (sec), leaf count = 18

dsolve(a*cos(diff(y(x),x))+b*diff(y(x),x)+x=0,y(x))
 

\[y \left (x \right ) = \int \operatorname {RootOf}\left (a \cos \left (\textit {\_Z} \right )+\textit {\_Z} b +x \right )d x +c_{1}\]