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 = 0.0133037 (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 = 0.007 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C2}\, \left ( x-{\frac {1}{2}} \right ) ^{1+{\frac {\sqrt {3}}{2}}}+{\it \_C3}\, \left ( x-{\frac {1}{2}} \right ) ^{1-{\frac {\sqrt {3}}{2}}}+{\it \_C1}\,x-{\frac {{\it \_C1}}{2}} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C2*(x-1/2)^(1+1/2*3^(1/2))+_C3*(x-1/2)^(1-1/2*3^(1/2))+_C1*x-1/2*_C1