\[ x y'(x)-y(x) f\left (x^a y(x)^b\right )=0 \] ✓ Mathematica : cpu = 466.579 (sec), leaf count = 183
\[\text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x \left (\frac {b^2 K[1]^{a-1} K[2]^{b-1} f'\left (K[1]^a K[2]^b\right )}{b f\left (K[1]^a K[2]^b\right )+a}-\frac {b^3 K[1]^{a-1} K[2]^{b-1} f\left (K[1]^a K[2]^b\right ) f'\left (K[1]^a K[2]^b\right )}{\left (b f\left (K[1]^a K[2]^b\right )+a\right )^2}\right ) \, dK[1]-\frac {b}{K[2] \left (b f\left (x^a K[2]^b\right )+a\right )}\right ) \, dK[2]+\int _1^x \frac {b f\left (y(x)^b K[1]^a\right )}{K[1] \left (b f\left (y(x)^b K[1]^a\right )+a\right )} \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.128 (sec), leaf count = 39
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{ \left ( f \left ( {x}^{a}{{\it \_a}}^{b} \right ) b+a \right ) {\it \_a}}}\,{\rm d}{\it \_a}-{\frac {\ln \left ( x \right ) }{b}}-{\it \_C1}=0 \right \} \]