\[ a y(x) y'(x)+x y(x) y''(x)-2 x y'(x)^2=0 \] ✓ Mathematica : cpu = 0.254411 (sec), leaf count = 34
DSolve[a*y[x]*Derivative[1][y][x] - 2*x*Derivative[1][y][x]^2 + x*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 \left (x^{1-a}+(a-1) c_1\right ){}^{\frac {a-1}{1-a}}\right \}\right \}\] ✓ Maple : cpu = 0.915 (sec), leaf count = 27
dsolve(x*y(x)*diff(diff(y(x),x),x)-2*x*diff(y(x),x)^2+a*y(x)*diff(y(x),x)=0,y(x))
\[y \left (x \right ) = -\frac {x^{a} \left (a -1\right )}{c_{2} \left (a -1\right ) x^{a}-c_{1} x}\]