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