\[ (f(y(x)+x)+1) y'(x)+f(y(x)+x)=0 \] ✓ Mathematica : cpu = 0.112949 (sec), leaf count = 52
\[\text {Solve}\left [\int _1^{y(x)}\left (f(x+K[2])-\int _1^xf'(K[1]+K[2])dK[1]+1\right )dK[2]+\int _1^xf(K[1]+y(x))dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.035 (sec), leaf count = 22
\[y \relax (x ) = -x +\RootOf \left (-x +\int _{}^{\textit {\_Z}}\left (1+f \left (\textit {\_a} \right )\right )d \textit {\_a} +c_{1}\right )\]