\[ y''(x)-a \left (x y'(x)-y(x)\right )^r=0 \] ✓ Mathematica : cpu = 0.403004 (sec), leaf count = 91
\[\left \{\left \{y(x)\to x \left (c_2-x \left (2-\frac {a (r-1) x^2}{c_1}\right ){}^{\frac {1}{r-1}} \left (x^{2 r-2} \left (-a (r-1) x^2+2 c_1\right )\right ){}^{\frac {1}{1-r}} \, _2F_1\left (-\frac {1}{2},\frac {1}{r-1};\frac {1}{2};\frac {a (r-1) x^2}{2 c_1}\right )\right )\right \}\right \}\] ✓ Maple : cpu = 3.466 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) = \left ( \int \!-{\frac {{x}^{2} \left ( r-1 \right ) a-{\it \_C1}}{2\,{x}^{2}}{2}^{{\frac {r}{r-1}}} \left ( - \left ( {x}^{2} \left ( r-1 \right ) a-{\it \_C1} \right ) ^{-1} \right ) ^{{\frac {r}{r-1}}}}\,{\rm d}x+{\it \_C2} \right ) x \right \} \]