\[ \boxed { \left ( 2\,{x}^{2}+6\,x+4 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 10\,{x}^{2}+21\,x+8 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 12\,{x}^{2}+17\,x+8 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 162.565643 (sec), leaf count = 57 \[ \left \{\left \{y(x)\to c_2 e^{-3 x} (x+2)^4 \left (\int _1^x \frac {e^{K[1]} (K[1]+1)^{3/2}}{(K[1]+2)^5} \, dK[1]\right )+c_1 e^{-3 x} (x+2)^4\right \}\right \} \]
Maple: cpu = 0.125 (sec), leaf count = 54 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-2\,x}} \left ( x+2 \right ) ^{4}{\it HeunC} \left ( -1,-{\frac {5}{2}},4,-{\frac {7}{4}},{ \frac {7}{2}},-1-x \right ) +{\it \_C2}\,{{\rm e}^{-2\,x}} \left ( x+2 \right ) ^{4} \left ( 1+x \right ) ^{{\frac {5}{2}}}{\it HeunC} \left ( - 1,{\frac {5}{2}},4,-{\frac {7}{4}},{\frac {7}{2}},-1-x \right ) \right \} \]