\[ a x^3 y'(x)-2 a x^2 y(x)+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.175172 (sec), leaf count = 119
\[\left \{\left \{y(x)\to \frac {1}{2} (\cosh (2 c_1)+\sinh (2 c_1)) \left (-\sqrt {2} \sqrt {a} x^2+2 \cosh (2 c_1)+2 \sinh (2 c_1)\right )\right \},\left \{y(x)\to \frac {\sqrt {a} x^2 \cosh (2 c_1)}{\sqrt {2}}+\frac {\sqrt {a} x^2 \sinh (2 c_1)}{\sqrt {2}}+\cosh ^2(2 c_1)+\sinh ^2(2 c_1)+2 \sinh (2 c_1) \cosh (2 c_1)\right \}\right \}\] ✓ Maple : cpu = 0.784 (sec), leaf count = 27
\[y \relax (x ) = -\frac {a \,x^{4}}{8}\]