\[ (2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)-3 x-1=0 \] ✓ Mathematica : cpu = 0.0287067 (sec), leaf count = 47
DSolve[-1 - 3*x - 12*y[x] - 2*(1 + 2*x)*Derivative[1][y][x] + (1 + 2*x)^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {-72 x^2-56 x-7}{192 (2 x+1)}+c_1 (2 x+1)^3+\frac {c_2}{2 x+1}\right \}\right \}\] ✓ Maple : cpu = 0.016 (sec), leaf count = 41
dsolve((2*x+1)^2*diff(diff(y(x),x),x)-2*(2*x+1)*diff(y(x),x)-12*y(x)-3*x-1=0,y(x))
\[y \left (x \right ) = \frac {c_{1}}{2 x +1}+\left (2 x +1\right )^{3} c_{2}+\frac {-72 x^{2}-56 x -7}{384 x +192}\]