\[ \left (2 x^2+6 x+4\right ) y''(x)+\left (10 x^2+21 x+8\right ) y'(x)+\left (12 x^2+17 x+8\right ) y(x)=0 \] ✓ Mathematica : cpu = 1.65887 (sec), leaf count = 58
DSolve[(8 + 17*x + 12*x^2)*y[x] + (8 + 21*x + 10*x^2)*Derivative[1][y][x] + (4 + 6*x + 2*x^2)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 e^{-3 x} (x+2)^4 \int _1^x\frac {e^{K[1]} (K[1]+1)^{3/2}}{(K[1]+2)^5}dK[1]+c_1 e^{-3 x} (x+2)^4\right \}\right \}\] ✓ Maple : cpu = 0.148 (sec), leaf count = 46
dsolve((2*x^2+6*x+4)*diff(diff(y(x),x),x)+(10*x^2+21*x+8)*diff(y(x),x)+(12*x^2+17*x+8)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-2 x} \left (x +2\right )^{4} \left (c_{2} \HeunC \left (-1, \frac {5}{2}, 4, -\frac {7}{4}, \frac {7}{2}, -1-x \right ) \left (1+x \right )^{\frac {5}{2}}+c_{1} \HeunC \left (-1, -\frac {5}{2}, 4, -\frac {7}{4}, \frac {7}{2}, -1-x \right )\right )\]