\[ -16 e^{x^2} x^4-12 y''(x)+y^{(4)}(x)+12 y(x)=0 \] ✓ Mathematica : cpu = 0.925313 (sec), leaf count = 1722
\[\left \{\left \{y(x)\to \frac {1}{12} e^{-\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x-\sqrt {2 \left (3+\sqrt {6}\right )} x-\sqrt {2 \left (3-\sqrt {6}\right )} x} \left (-2 \sqrt {3+\sqrt {6}} e^{\sqrt {2 \left (3+\sqrt {6}\right )} x+2 \sqrt {2 \left (3-\sqrt {6}\right )} x} x^3+2 \sqrt {3+\sqrt {6}} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3-\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3+\sqrt {6}\right )} x} x^3+2 \sqrt {3-\sqrt {6}} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x-\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+2 \sqrt {2 \left (3+\sqrt {6}\right )} x+\sqrt {2 \left (3-\sqrt {6}\right )} x} x^3-2 \sqrt {3-\sqrt {6}} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3-\sqrt {6}\right )} x} x^3-\sqrt {2 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\sqrt {2 \left (3+\sqrt {6}\right )} x+2 \sqrt {2 \left (3-\sqrt {6}\right )} x} x^2-\sqrt {2 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3-\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3+\sqrt {6}\right )} x} x^2+\sqrt {2 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x-\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+2 \sqrt {2 \left (3+\sqrt {6}\right )} x+\sqrt {2 \left (3-\sqrt {6}\right )} x} x^2+\sqrt {2 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3-\sqrt {6}\right )} x} x^2+\sqrt {6 \left (3+\sqrt {6}\right )} e^{\sqrt {2 \left (3+\sqrt {6}\right )} x+2 \sqrt {2 \left (3-\sqrt {6}\right )} x} x-\sqrt {6 \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3-\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3+\sqrt {6}\right )} x} x+\sqrt {6 \left (3-\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x-\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+2 \sqrt {2 \left (3+\sqrt {6}\right )} x+\sqrt {2 \left (3-\sqrt {6}\right )} x} x-\sqrt {6 \left (3-\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3-\sqrt {6}\right )} x} x+\sqrt {3 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\sqrt {2 \left (3+\sqrt {6}\right )} x+2 \sqrt {2 \left (3-\sqrt {6}\right )} x}+\sqrt {2 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\sqrt {2 \left (3+\sqrt {6}\right )} x+2 \sqrt {2 \left (3-\sqrt {6}\right )} x}+\sqrt {3 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3-\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3+\sqrt {6}\right )} x}+\sqrt {2 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3-\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3+\sqrt {6}\right )} x}+\sqrt {3 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x-\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+2 \sqrt {2 \left (3+\sqrt {6}\right )} x+\sqrt {2 \left (3-\sqrt {6}\right )} x}-\sqrt {2 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x-\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+2 \sqrt {2 \left (3+\sqrt {6}\right )} x+\sqrt {2 \left (3-\sqrt {6}\right )} x}+\sqrt {3 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3-\sqrt {6}\right )} x}-\sqrt {2 \left (3-\sqrt {6}\right ) \left (3+\sqrt {6}\right )} e^{\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x+\left (x+\sqrt {2 \left (3+\sqrt {6}\right )}\right ) x+\sqrt {2 \left (3-\sqrt {6}\right )} x}\right )+e^{\sqrt {2 \left (3-\sqrt {6}\right )} x} c_1+e^{-\sqrt {2 \left (3-\sqrt {6}\right )} x} c_2+e^{\sqrt {2 \left (3+\sqrt {6}\right )} x} c_3+e^{-\sqrt {2 \left (3+\sqrt {6}\right )} x} c_4\right \}\right \}\] ✓ Maple : cpu = 0.112 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{x}^{2}}}+{\it \_C1}\,{{\rm e}^{\sqrt {6-2\,\sqrt {6}}x}}+{\it \_C2}\,{{\rm e}^{\sqrt {6+2\,\sqrt {6}}x}}+{\it \_C3}\,{{\rm e}^{-\sqrt {6-2\,\sqrt {6}}x}}+{\it \_C4}\,{{\rm e}^{-\sqrt {6+2\,\sqrt {6}}x}} \right \} \]