\[ (f(y(x)+x)+1) y'(x)+f(y(x)+x)=0 \] ✓ Mathematica : cpu = 0.103035 (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 = 0.03 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) =-x+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!1+f \left ( {\it \_a} \right ) {d{\it \_a}}+{\it \_C1} \right ) \right \} \]