\[ \left (2 x^2+6 x+4\right ) y''(x)+\left (10 x^2+21 x+8\right ) y'(x)+\left (12 x^2+17 x+8\right ) y(x)=0 \] ✓ Mathematica : cpu = 1.85336 (sec), leaf count = 58
\[\left \{\left \{y(x)\to c_2 e^{-3 x} (x+2)^4 \int _1^x\frac {e^{K[1]} (K[1]+1)^{3/2}}{(K[1]+2)^5}dK[1]+c_1 e^{-3 x} (x+2)^4\right \}\right \}\] ✓ Maple : cpu = 0.107 (sec), leaf count = 46
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-2\,x}} \left ( x+2 \right ) ^{4} \left ( {\it \_C2}\,{\it HeunC} \left ( -1,{\frac {5}{2}},4,-{\frac {7}{4}},{\frac {7}{2}},-1-x \right ) \left ( 1+x \right ) ^{{\frac {5}{2}}}+{\it \_C1}\,{\it HeunC} \left ( -1,-{\frac {5}{2}},4,-{\frac {7}{4}},{\frac {7}{2}},-1-x \right ) \right ) \right \} \]