\[ a x^2 y'(x)^2-(a-1) a x^2-2 a x y(x) y'(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 0.422821 (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 = 0.154 (sec), leaf count = 106
\[\left \{y \left (x \right ) = x \RootOf \left (c_{1}-\left (\int _{}^{\textit {\_Z}}\frac {\sqrt {\left (a -1\right ) \left (\textit {\_a}^{2}+a \right ) a}}{\left (a -1\right ) \left (\textit {\_a}^{2}+a \right )}d \textit {\_a} \right )-\ln \left (x \right )\right ), y \left (x \right ) = x \RootOf \left (c_{1}+\int _{}^{\textit {\_Z}}\frac {\sqrt {\left (a -1\right ) \left (\textit {\_a}^{2}+a \right ) a}}{\left (a -1\right ) \left (\textit {\_a}^{2}+a \right )}d \textit {\_a} -\ln \left (x \right )\right ), y \left (x \right ) = \sqrt {-a}\, x, y \left (x \right ) = -\sqrt {-a}\, x\right \}\]