\[ y''(x)-a \left (x y'(x)-y(x)\right )^r=0 \] ✓ Mathematica : cpu = 0.507856 (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 = 0.69 (sec), leaf count = 60
\[\left \{y \left (x \right ) = \left (c_{2}+\int -\frac {\left (\left (r -1\right ) a \,x^{2}-c_{1}\right ) 2^{\frac {r}{r -1}} \left (-\frac {1}{\left (r -1\right ) a \,x^{2}-c_{1}}\right )^{\frac {r}{r -1}}}{2 x^{2}}d x \right ) x\right \}\]