\[ \boxed { 2\,{x}^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\, \left ( y \left ( x \right ) \right ) ^{2}-3\,xy \left ( x \right ) +2\,{a}^{2}x=0} \]
Mathematica: cpu = 0.082010 (sec), leaf count = 131 \[ \left \{\left \{y(x)\to -\frac {x^2 \left (c_1 \left (\frac {a e^{-\frac {2 a}{\sqrt {x}}}}{x}+\frac {e^{-\frac {2 a}{\sqrt {x}}}}{2 \sqrt {x}}\right )-\frac {e^{\frac {2 a}{\sqrt {x}}}}{4 a \sqrt {x}}+\frac {e^{\frac {2 a}{\sqrt {x}}}}{2 x}\right )}{c_1 \sqrt {x} e^{-\frac {2 a}{\sqrt {x}}}-\frac {\sqrt {x} e^{\frac {2 a}{\sqrt {x}}}}{2 a}}\right \}\right \} \]
Maple: cpu = 0.156 (sec), leaf count = 102 \[ \left \{ y \left ( x \right ) ={1 \left ( \left ( -2\,x{\it \_C1}\,\sqrt {-{\frac {{a}^{2}}{x}}}-x \right ) \sin \left ( 2\,\sqrt {-{\frac {{a}^{ 2}}{x}}} \right ) -x \left ( {\it \_C1}-2\,\sqrt {-{\frac {{a}^{2}}{x}}} \right ) \cos \left ( 2\,\sqrt {-{\frac {{a}^{2}}{x}}} \right ) \right ) \left ( 2\,\cos \left ( 2\,\sqrt {-{\frac {{a}^{2}}{x}}} \right ) {\it \_C1}+2\,\sin \left ( 2\,\sqrt {-{\frac {{a}^{2}}{x}}} \right ) \right ) ^{-1}} \right \} \]