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 = 0.0346516 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {192 c_1 (2 x+1)^4+192 c_2-72 x^2-56 x-7}{192 (2 x+1)}\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{1+2\,x}}+ \left ( 1+2\,x \right ) ^{3}{\it \_C2}+{\frac {-72\,{x}^{2}-56\,x-7}{192+384\,x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/(1+2*x)*_C1+(1+2*x)^3*_C2+(-72*x^2-56*x-7)/(192+384*x)