ODE
\[ (1-2 x) y''(x)-(x+2) y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.16098 (sec), leaf count = 50
\[\left \{\left \{y(x)\to e^{-x/2} \left (c_2 L_{-\frac {1}{4}}^{\frac {1}{4}}\left (\frac {x}{2}-\frac {1}{4}\right )+\frac {\sqrt {2} c_1}{\sqrt [4]{2 x-1}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.728 (sec), leaf count = 34
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {x}{2}} \hypergeom \left (\left [\frac {1}{4}\right ], \left [\frac {5}{4}\right ], -\frac {1}{4}+\frac {x}{2}\right )+\frac {\textit {\_C2} \,{\mathrm e}^{-\frac {x}{2}}}{\left (-1+2 x \right )^{\frac {1}{4}}}\right ]\] Mathematica raw input
DSolve[-y[x] - (2 + x)*y'[x] + (1 - 2*x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((Sqrt[2]*C[1])/(-1 + 2*x)^(1/4) + C[2]*LaguerreL[-1/4, 1/4, -1/4 + x/2])/E^(x/2)}}
Maple raw input
dsolve((1-2*x)*diff(diff(y(x),x),x)-(2+x)*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(-1/2*x)*hypergeom([1/4],[5/4],-1/4+1/2*x)+_C2*exp(-1/2*x)/(-1+2*x)^(1/4)]