ODE
\[ (1-2 x)^3 y'''(x)+(1-2 x) y'(x)+2 y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.156379 (sec), leaf count = 50
\[\left \{\left \{y(x)\to (2 x-1) \left (c_2 (2 x-1)^{\frac {\sqrt {3}}{2}}+c_1 (2 x-1)^{-\frac {\sqrt {3}}{2}}+c_3\right )\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 36
\[\left [y \left (x \right ) = \textit {\_C1} \left (-\frac {1}{2}+x \right )+\textit {\_C2} \left (-\frac {1}{2}+x \right )^{1+\frac {\sqrt {3}}{2}}+\textit {\_C3} \left (-\frac {1}{2}+x \right )^{1-\frac {\sqrt {3}}{2}}\right ]\] Mathematica raw input
DSolve[2*y[x] + (1 - 2*x)*y'[x] + (1 - 2*x)^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + 2*x)*(C[1]/(-1 + 2*x)^(Sqrt[3]/2) + (-1 + 2*x)^(Sqrt[3]/2)*C[2] + C[3])}}
Maple raw input
dsolve((1-2*x)^3*diff(diff(diff(y(x),x),x),x)+(1-2*x)*diff(y(x),x)+2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(-1/2+x)+_C2*(-1/2+x)^(1+1/2*3^(1/2))+_C3*(-1/2+x)^(1-1/2*3^(1/2))]