\[ -a x y(x) y'(x)+2 a y(x)^2+y'(x)^2=0 \] ✓ Mathematica : cpu = 5.95425 (sec), leaf count = 121
\[\left \{\left \{y(x)\to \frac {c_1 e^{\frac {1}{4} \left (a x^2+\sqrt {a} x \sqrt {a x^2-8}\right )}}{\left (\sqrt {a} \sqrt {a x^2-8}+a x\right )^2}\right \},\left \{y(x)\to a c_1 e^{\frac {1}{4} \left (a x^2-\sqrt {a} x \sqrt {a x^2-8}\right )} \left (\sqrt {a x^2-8}+\sqrt {a} x\right )^2\right \}\right \}\]
✓ Maple : cpu = 0.625 (sec), leaf count = 122
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {{a}^{2}x{\frac {1}{\sqrt {{a}^{2}}}}}+\sqrt {{a}^{2}{x}^{2}-8\,a} \right ) ^{-2\,{\frac {a}{\sqrt {{a}^{2}}}}}{{\rm e}^{{\frac {x}{4} \left ( ax+\sqrt {{a}^{2}{x}^{2}-8\,a} \right ) }}},y \left ( x \right ) ={\it \_C1}\, \left ( {{a}^{2}x{\frac {1}{\sqrt {{a}^{2}}}}}+\sqrt {{a}^{2}{x}^{2}-8\,a} \right ) ^{2\,{\frac {a}{\sqrt {{a}^{2}}}}}{{\rm e}^{-{\frac {x}{4}\sqrt {{a}^{2}{x}^{2}-8\,a}}+{\frac {a{x}^{2}}{4}}}} \right \} \]