\[ \left (2 x^2+6 x+4\right ) y''(x)+\left (10 x^2+21 x+8\right ) y'(x)+\left (12 x^2+17 x+8\right ) y(x)=0 \] ✓ Mathematica : cpu = 1.65887 (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 = 0.148 (sec), leaf count = 46
\[y \relax (x ) = {\mathrm e}^{-2 x} \left (x +2\right )^{4} \left (c_{2} \HeunC \left (-1, \frac {5}{2}, 4, -\frac {7}{4}, \frac {7}{2}, -1-x \right ) \left (1+x \right )^{\frac {5}{2}}+c_{1} \HeunC \left (-1, -\frac {5}{2}, 4, -\frac {7}{4}, \frac {7}{2}, -1-x \right )\right )\]