\[ a x^3 y'(x)-2 a x^2 y(x)+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.25678 (sec), leaf count = 119
\[\left \{\left \{y(x)\to \frac {1}{2} \left (\sinh \left (2 c_1\right )+\cosh \left (2 c_1\right )\right ) \left (-\sqrt {2} \sqrt {a} x^2+2 \sinh \left (2 c_1\right )+2 \cosh \left (2 c_1\right )\right )\right \},\left \{y(x)\to \frac {\sqrt {a} x^2 \sinh \left (2 c_1\right )}{\sqrt {2}}+\frac {\sqrt {a} x^2 \cosh \left (2 c_1\right )}{\sqrt {2}}+\sinh ^2\left (2 c_1\right )+\cosh ^2\left (2 c_1\right )+2 \sinh \left (2 c_1\right ) \cosh \left (2 c_1\right )\right \}\right \}\] ✓ Maple : cpu = 3.201 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{4}}{8}},y \left ( x \right ) ={\it \_C1}\,{x}^{2}+2\,{\frac {{{\it \_C1}}^{2}}{a}} \right \} \]