\[ \left (x^2-a^2\right ) y''(x)+8 x y'(x)+12 y(x)=0 \] ✓ Mathematica : cpu = 0.0364992 (sec), leaf count = 41
DSolve[12*y[x] + 8*x*Derivative[1][y][x] + (-a^2 + x^2)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_2 \left (a^2+3 x^2\right )}{3 (a-x)^3 (a+x)^3}+\frac {c_1}{(a+x)^3}\right \}\right \}\] ✓ Maple : cpu = 0.021 (sec), leaf count = 41
dsolve((-a^2+x^2)*diff(diff(y(x),x),x)+8*x*diff(y(x),x)+12*y(x)=0,y(x))
\[y \left (x \right ) = \frac {3 a^{2} x c_{2}+x^{3} c_{2}+a^{2} c_{1}+3 c_{1} x^{2}}{\left (a -x \right )^{3} \left (x +a \right )^{3}}\]