\[ y'(x)-x^{a-1} y(x)^{1-b} f\left (\frac {x^a}{a}+\frac {y(x)^b}{b}\right )=0 \] ✓ Mathematica : cpu = 0.435531 (sec), leaf count = 238
\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]^{b-1}}{f\left (\frac {x^a}{a}+\frac {K[2]^b}{b}\right )+1}-\int _1^x\left (\frac {K[1]^{a-1} K[2]^{b-1} f'\left (\frac {K[1]^a}{a}+\frac {K[2]^b}{b}\right )}{f\left (\frac {K[1]^a}{a}+\frac {K[2]^b}{b}\right )+1}-\frac {f\left (\frac {K[1]^a}{a}+\frac {K[2]^b}{b}\right ) K[1]^{a-1} K[2]^{b-1} f'\left (\frac {K[1]^a}{a}+\frac {K[2]^b}{b}\right )}{\left (f\left (\frac {K[1]^a}{a}+\frac {K[2]^b}{b}\right )+1\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {f\left (\frac {K[1]^a}{a}+\frac {y(x)^b}{b}\right ) K[1]^{a-1}}{f\left (\frac {K[1]^a}{a}+\frac {y(x)^b}{b}\right )+1}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.427 (sec), leaf count = 153
\[\left \{y \left (x \right ) = \left (-\frac {-a \RootOf \left (c_{1} a b +a^{2} \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \left (a^{\frac {1}{a}}\right )^{a} \left (\left (\textit {\_a} -b \right )^{\frac {1}{b}}\right )^{-b} f \left (\frac {a \left (\left (\textit {\_a} -b \right )^{\frac {1}{b}}\right )^{b}+b \left (a^{\frac {1}{a}}\right )^{a}}{a b}\right )-b \left (a^{\frac {1}{a}}\right )^{a} \left (\left (\textit {\_a} -b \right )^{\frac {1}{b}}\right )^{-b} f \left (\frac {a \left (\left (\textit {\_a} -b \right )^{\frac {1}{b}}\right )^{b}+b \left (a^{\frac {1}{a}}\right )^{a}}{a b}\right )+a}d \textit {\_a} \right )-b \,x^{a}\right )+b \,x^{a}}{a}\right )^{\frac {1}{b}}\right \}\]