\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -a \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \right ) ^{r}=0} \]
Mathematica: cpu = 48.122611 (sec), leaf count = 59 \[ \left \{\left \{y(x)\to x \left (\int _1^x \left (\frac {1}{2} a K[2]^{2 r}-\frac {1}{2} a r K[2]^{2 r}+c_1 K[2]^{2 r-2}\right ){}^{\frac {1}{1-r}} \, dK[2]+c_2\right )\right \}\right \} \]
Maple: cpu = 0.312 (sec), leaf count = 123 \[ \left \{ y \left ( x \right ) = \left ( \int \!-{\frac {ar}{2}{2}^{{ \frac {r}{r-1}}} \left ( \left ( -ar{x}^{2}+a{x}^{2}+{\it \_C1} \right ) ^{-1} \right ) ^{{\frac {r}{r-1}}}}+{\frac {a}{2}{2}^{{\frac { r}{r-1}}} \left ( \left ( -ar{x}^{2}+a{x}^{2}+{\it \_C1} \right ) ^{-1} \right ) ^{{\frac {r}{r-1}}}}+{\frac {{\it \_C1}}{2\,{x}^{2}}{2}^{{ \frac {r}{r-1}}} \left ( \left ( -ar{x}^{2}+a{x}^{2}+{\it \_C1} \right ) ^{-1} \right ) ^{{\frac {r}{r-1}}}}\,{\rm d}x+{\it \_C2} \right ) x \right \} \]