\[ -16 e^{x^2} x^4+y^{(4)}(x)-12 y''(x)+12 y(x)=0 \] ✓ Mathematica : cpu = 0.888141 (sec), leaf count = 1722
\[\left \{\left \{y(x)\to \frac {1}{12} e^{-\left (\left (\sqrt {2 \left (3-\sqrt {6}\right )}-x\right ) x\right )-\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 = 0.125 (sec), leaf count = 67
\[y \relax (x ) = {\mathrm e}^{x^{2}}+c_{1} {\mathrm e}^{\sqrt {6-2 \sqrt {6}}\, x}+c_{2} {\mathrm e}^{\sqrt {6+2 \sqrt {6}}\, x}+c_{3} {\mathrm e}^{-\sqrt {6-2 \sqrt {6}}\, x}+c_{4} {\mathrm e}^{-\sqrt {6+2 \sqrt {6}}\, x}\]