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