\[ \boxed { x \left ( {x}^{2}+2 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -6\,xy \left ( x \right ) =0} \]
Mathematica: cpu = 0.099513 (sec), leaf count = 118 \[ \left \{\left \{y(x)\to \frac {c_2 \left (-2 \sqrt [4]{2} x^2 \, _2F_1\left (\frac {1}{4},\frac {3}{4};\frac {5}{4};-\frac {x^2}{2}\right )-\sqrt [4]{2} x^4 \, _2F_1\left (\frac {1}{4},\frac {3}{4};\frac {5}{4};-\frac {x^2}{2}\right )-\sqrt [4]{x^2+2} x^2-\sqrt [4]{x^2+2}\right )}{3 \sqrt [4]{x^2+2}}+c_1 \left (x^2+2\right )^{3/4} x^{3/2}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {3}{2}}} \left ( { x}^{2}+2 \right ) ^{{\frac {3}{4}}}+{\it \_C2}\, \left ( {x}^{2}+2 \right ) ^{{\frac {3}{4}}} {\mbox {$_2$F$_1$}(-{\frac {3}{4}},{\frac {7}{4}};\,{\frac {1}{4}};\,-{\frac {{x}^{2}}{2}})} \right \} \]