\[ y'(x)-x^{a-1} y(x)^{1-b} f\left (\frac {x^a}{a}+\frac {y(x)^b}{b}\right )=0 \] ✓ Mathematica : cpu = 197.699 (sec), leaf count = 182
\[\text {Solve}\left [c_1=\int _1^{y(x)} -\frac {K[2] \left (f\left (\frac {K[2]^b}{b}+\frac {x^a}{a}\right )+1\right ) \left (\int _1^x \frac {K[1]^{a-1} K[2]^{b-1} f'\left (\frac {K[1]^a}{a}+\frac {K[2]^b}{b}\right )}{\left (f\left (\frac {K[1]^a}{a}+\frac {K[2]^b}{b}\right )+1\right )^2} \, dK[1]\right )+K[2]^b}{K[2] \left (f\left (\frac {K[2]^b}{b}+\frac {x^a}{a}\right )+1\right )} \, dK[2]+\int _1^x \frac {K[1]^{a-1} f\left (\frac {K[1]^a}{a}+\frac {y(x)^b}{b}\right )}{f\left (\frac {K[1]^a}{a}+\frac {y(x)^b}{b}\right )+1} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.468 (sec), leaf count = 153
\[ \left \{ y \left ( x \right ) =\sqrt [b]{-{\frac {1}{a} \left ( -{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( \left ( \sqrt [b]{-b+{\it \_a}} \right ) ^{-b} \left ( \sqrt [a]{a} \right ) ^{a}f \left ( {\frac { \left ( \sqrt [a]{a} \right ) ^{a}b+ \left ( \sqrt [b]{-b+{\it \_a}} \right ) ^{b}a}{ab}} \right ) {\it \_a}- \left ( \sqrt [b]{-b+{\it \_a}} \right ) ^{-b} \left ( \sqrt [a]{a} \right ) ^{a}f \left ( {\frac { \left ( \sqrt [a]{a} \right ) ^{a}b+ \left ( \sqrt [b]{-b+{\it \_a}} \right ) ^{b}a}{ab}} \right ) b+a \right ) ^{-1}{d{\it \_a}}{a}^{2}+{\it \_C1}\,ab-{x}^{a}b \right ) a+{x}^{a}b \right ) }} \right \} \]