\[ y''(x)-a \left (x y'(x)-y(x)\right )^r=0 \] ✓ Mathematica : cpu = 52.4589 (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 = 0.785 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) = \left ( \int \!-{\frac {{x}^{2} \left ( r-1 \right ) a-{\it \_C1}}{2\,{x}^{2}}{2}^{{\frac {r}{r-1}}} \left ( - \left ( {x}^{2} \left ( r-1 \right ) a-{\it \_C1} \right ) ^{-1} \right ) ^{{\frac {r}{r-1}}}}\,{\rm d}x+{\it \_C2} \right ) x \right \} \]