\[ y''(x)-a \left (x y'(x)-y(x)\right )^r=0 \] ✓ Mathematica : cpu = 0.380774 (sec), leaf count = 60
DSolve[-(a*(-y[x] + x*Derivative[1][y][x])^r) + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to x \left (\int _1^x\left (\frac {1}{2} a K[2]^{2 r}-\frac {1}{2} a r K[2]^{2 r}+c_1 K[2]^{2 r-2}\right ){}^{\frac {1}{1-r}}dK[2]+c_2\right )\right \}\right \}\] ✓ Maple : cpu = 4.752 (sec), leaf count = 60
dsolve(diff(diff(y(x),x),x)-a*(x*diff(y(x),x)-y(x))^r=0,y(x))
\[y \left (x \right ) = \left (\int -\frac {2^{\frac {r}{r -1}} \left (\left (r -1\right ) a \,x^{2}-c_{1}\right ) \left (-\frac {1}{\left (r -1\right ) a \,x^{2}-c_{1}}\right )^{\frac {r}{r -1}}}{2 x^{2}}d x +c_{2}\right ) x\]