\[ \boxed { \left ( 1+x \right ) {x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( 4\,x+2 \right ) {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 10\,x+4 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -4\, \left ( 3\,x+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.065008 (sec), leaf count = 35 \[ \left \{\left \{y(x)\to c_1 x^2+c_3 x^2 \left (x+\frac {1}{x}+\log ^2(x)\right )+c_2 x^2 \log (x)\right \}\right \} \]
Maple: cpu = 0.358 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}+{\it \_C2}\,{x}^{2} \ln \left ( x \right ) +{\it \_C3}\, \left ( x \left ( \ln \left ( x \right ) \right ) ^{2}+{x}^{2}+1 \right ) x \right \} \]