\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\,y \left ( x \right ) -4\,{x}^{2}{{\rm e}^{{x}^{2}}}=0} \]
Mathematica: cpu = 0.057007 (sec), leaf count = 135 \[ \left \{\left \{y(x)\to c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x}+\frac {e^{-\sqrt {2} x} \left (-2 e^{x \left (x+\sqrt {2}\right )} x+2 e^{\left (x-\sqrt {2}\right ) x+2 \sqrt {2} x} x+\sqrt {2} e^{x \left (x+\sqrt {2}\right )}+\sqrt {2} e^{\left (x-\sqrt {2}\right ) x+2 \sqrt {2} x}\right )}{2 \sqrt {2}}\right \}\right \} \]
Maple: cpu = 0.016 (sec), leaf count = 26 \[ \left \{ y \left ( x \right ) ={{\rm e}^{x\sqrt {2}}}{\it \_C2}+{{\rm e} ^{-x\sqrt {2}}}{\it \_C1}+{{\rm e}^{{x}^{2}}} \right \} \]