ODE
\[ (2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.17297 (sec), leaf count = 26
\[\left \{\left \{y(x)\to c_1 (2 x+1)^3+\frac {c_2}{2 x+1}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x +\frac {1}{2}}+\textit {\_C2} \left (x +\frac {1}{2}\right )^{3}\right ]\] Mathematica raw input
DSolve[-12*y[x] - 2*(1 + 2*x)*y'[x] + (1 + 2*x)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 + 2*x)^3*C[1] + C[2]/(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) = 0, y(x))
Maple raw output
[y(x) = _C1/(x+1/2)+_C2*(x+1/2)^3]