\[ a y(x) y'(x)+x y(x) y''(x)+2 x y'(x)^2=0 \] ✓ Mathematica : cpu = 0.234885 (sec), leaf count = 40
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]
\[\left \{\left \{y(x)\to c_2 \left (3 x^{1-a}-(a-1) c_1\right ){}^{-\frac {a-1}{3 (1-a)}}\right \}\right \}\] ✓ Maple : cpu = 0.938 (sec), leaf count = 148
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))
\[y \left (x \right ) = \frac {x^{-a} 3^{\frac {1}{3}} \left (\left (a -1\right )^{2} \left (c_{2} \left (a -1\right ) x^{a}-c_{1} x \right ) x^{2 a}\right )^{\frac {1}{3}}}{a -1}\]