\[ \boxed { 4\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +8\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( 4\,{x}^{2}+12\,x+3 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.039005 (sec), leaf count = 52 \[ \left \{\left \{y(x)\to \frac {c_2 e^{-x} \left (4 e^{2 x} x^2 \text {Ei}(-2 x)+2 x-1\right )}{2 x^{3/2}}+c_1 e^x \sqrt {x}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}{{\rm e}^{x}}+{{\it \_C2}\, \left ( 4\,{x}^{2}{{\rm e}^{x}}{\it Ei} \left ( 1,2\,x \right ) - 2\,{{\rm e}^{-x}}x+{{\rm e}^{-x}} \right ) {x}^{-{\frac {3}{2}}}} \right \} \]