\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -f \left ( ax+by \left ( x \right ) \right ) =0} \]
Mathematica: cpu = 8.757112 (sec), leaf count = 244 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {b f(b K[2]+a x) \left (\int _1^x \left (\frac {b^2 f'(a K[1]+b K[2])}{b f(a K[1]+b K[2])+a}-\frac {b^3 f(a K[1]+b K[2]) f'(a K[1]+b K[2])}{(b f(a K[1]+b K[2])+a)^2}\right ) \, dK[1]\right )+a \int _1^x \left (\frac {b^2 f'(a K[1]+b K[2])}{b f(a K[1]+b K[2])+a}-\frac {b^3 f(a K[1]+b K[2]) f'(a K[1]+b K[2])}{(b f(a K[1]+b K[2])+a)^2}\right ) \, dK[1]+b}{b f(b K[2]+a x)+a} \, dK[2]+\int _1^x \frac {b f(a K[1]+b y(x))}{b f(a K[1]+b y(x))+a} \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( f \left ( {\it \_a}\,b \right ) b+a \right ) ^{-1}{d{\it \_a}}b-x+{\it \_C1} \right ) b-ax}{b}} \right \} \]