ODE
\[ (1-2 x) (1-x) x^2 y''(x)+2 (1-2 x) (2-x) x y'(x)+2 (1-x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0539122 (sec), leaf count = 43
\[\left \{\left \{y(x)\to \frac {c_1 (4-8 x)-2 c_2 (x-1) x+c_2 (2 x-1) \log (1-2 x)}{4 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.029 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\frac { \left ( -4\,x+2 \right ) {\it \_C2}\,\ln \left ( -1+2\,x \right ) + \left ( 4\,{x}^{2}-2\,x-1 \right ) {\it \_C2}+2\,{\it \_C1}\,x-{\it \_C1}}{{x}^{2}}} \right \} \] Mathematica raw input
DSolve[2*(1 - x)*y[x] + 2*(1 - 2*x)*(2 - x)*x*y'[x] + (1 - 2*x)*(1 - x)*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((4 - 8*x)*C[1] - 2*(-1 + x)*x*C[2] + (-1 + 2*x)*C[2]*Log[1 - 2*x])/(4*x^2)}}
Maple raw input
dsolve(x^2*(1-x)*(1-2*x)*diff(diff(y(x),x),x)+2*x*(2-x)*(1-2*x)*diff(y(x),x)+2*(1-x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ((-4*x+2)*_C2*ln(-1+2*x)+(4*x^2-2*x-1)*_C2+2*_C1*x-_C1)/x^2