\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -4\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 4\,{x}^{2}-3 \right ) y \left ( x \right ) -{{\rm e}^{{x}^{2}}}=0} \]
Mathematica: cpu = 0.030004 (sec), leaf count = 44 \[ \left \{\left \{y(x)\to c_1 e^{(x-1) x}+\frac {1}{2} c_2 e^{(x-1) x+2 x}-e^{(x-1) x+x}\right \}\right \} \]
Maple: cpu = 0.032 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) ={{\rm e}^{x \left ( 1+x \right ) }}{\it \_C2}+{{\rm e}^{x \left ( x-1 \right ) }}{\it \_C1}-{{\rm e}^{{x}^{2}}} \right \} \]