\[ a x^2 y'(x)^2-(a-1) a x^2-2 a x y(x) y'(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 0.376706 (sec), leaf count = 241
DSolve[-((-1 + a)*a*x^2) + y[x]^2 - 2*a*x*y[x]*Derivative[1][y][x] + a*x^2*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {a} e^{-c_1} x^{1-\sqrt {\frac {a-1}{a}}} \left (-x^{2 \sqrt {\frac {a-1}{a}}}+e^{2 c_1}\right )\right \},\left \{y(x)\to \frac {1}{2} \sqrt {a} e^{-c_1} x^{1-\sqrt {\frac {a-1}{a}}} \left (-x^{2 \sqrt {\frac {a-1}{a}}}+e^{2 c_1}\right )\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {a} e^{-c_1} x^{1-\sqrt {\frac {a-1}{a}}} \left (-1+e^{2 c_1} x^{2 \sqrt {\frac {a-1}{a}}}\right )\right \},\left \{y(x)\to \frac {1}{2} \sqrt {a} e^{-c_1} x^{1-\sqrt {\frac {a-1}{a}}} \left (-1+e^{2 c_1} x^{2 \sqrt {\frac {a-1}{a}}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.148 (sec), leaf count = 106
dsolve(a*x^2*diff(y(x),x)^2-2*a*x*y(x)*diff(y(x),x)+y(x)^2-a*(a-1)*x^2 = 0,y(x))
\[y \left (x \right ) = \sqrt {-a}\, x\]