ODE
\[ (1-2 x) (1-x) y''(x)+2 (1-2 x) y'(x)+4 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.192044 (sec), leaf count = 39
\[\left \{\left \{y(x)\to c_1 (2 x-1)+\frac {1}{4} c_2 (2 (x-1) x+(1-2 x) \log (1-2 x))\right \}\right \}\]
Maple ✓
cpu = 0.067 (sec), leaf count = 37
\[\left [y \left (x \right ) = \textit {\_C1} \left (1-2 x \right )+\textit {\_C2} \left (\frac {\left (-4 x +2\right ) \ln \left (-1+2 x \right )}{8}+\frac {x^{2}}{2}-\frac {x}{4}-\frac {1}{8}\right )\right ]\] Mathematica raw input
DSolve[4*y[x] + 2*(1 - 2*x)*y'[x] + (1 - 2*x)*(1 - x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + 2*x)*C[1] + (C[2]*(2*(-1 + x)*x + (1 - 2*x)*Log[1 - 2*x]))/4}}
Maple raw input
dsolve((1-x)*(1-2*x)*diff(diff(y(x),x),x)+2*(1-2*x)*diff(y(x),x)+4*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(1-2*x)+_C2*(1/8*(-4*x+2)*ln(-1+2*x)+1/2*x^2-1/4*x-1/8)]