ODE
\[ (2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=3 x+1 \] ODE Classification
[[_2nd_order, _exact, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.175484 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {-72 x^2-56 x+192 c_1 (2 x+1)^4-7+192 c_2}{192 (2 x+1)}\right \}\right \}\]
Maple ✓
cpu = 0.11 (sec), leaf count = 42
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{1+2 x}+\left (1+2 x \right )^{3} \textit {\_C2} -\frac {72 x^{2}+56 x +7}{192 \left (1+2 x \right )}\right ]\] Mathematica raw input
DSolve[-12*y[x] - 2*(1 + 2*x)*y'[x] + (1 + 2*x)^2*y''[x] == 1 + 3*x,y[x],x]
Mathematica raw output
{{y[x] -> (-7 - 56*x - 72*x^2 + 192*(1 + 2*x)^4*C[1] + 192*C[2])/(192*(1 + 2*x))}}
Maple raw input
dsolve((1+2*x)^2*diff(diff(y(x),x),x)-2*(1+2*x)*diff(y(x),x)-12*y(x) = 1+3*x, y(x))
Maple raw output
[y(x) = 1/(1+2*x)*_C1+(1+2*x)^3*_C2-1/192*(72*x^2+56*x+7)/(1+2*x)]