\[ -16 e^{x^2} x^4+y^{(4)}(x)-12 y''(x)+12 y(x)=0 \] ✓ Mathematica : cpu = 0.933025 (sec), leaf count = 93
\[\left \{\left \{y(x)\to c_1 e^{\sqrt {6-2 \sqrt {6}} x}+c_2 e^{-\sqrt {6-2 \sqrt {6}} x}+c_3 e^{\sqrt {2 \left (3+\sqrt {6}\right )} x}+c_4 e^{-\sqrt {2 \left (3+\sqrt {6}\right )} x}+e^{x^2}\right \}\right \}\]
✓ Maple : cpu = 0.147 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{x}^{2}}}+{\it \_C1}\,{{\rm e}^{\sqrt {6-2\,\sqrt {6}}x}}+{\it \_C2}\,{{\rm e}^{\sqrt {6+2\,\sqrt {6}}x}}+{\it \_C3}\,{{\rm e}^{-\sqrt {6-2\,\sqrt {6}}x}}+{\it \_C4}\,{{\rm e}^{-\sqrt {6+2\,\sqrt {6}}x}} \right \} \]