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 = 0.0413675 (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 = 0.048 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 2-4\,x \right ) {\it \_C2}\,\ln \left ( -1+2\,x \right ) }{8}}+{\frac { \left ( 4\,{x}^{2}-2\,x-1 \right ) {\it \_C2}}{8}}-2\,{\it \_C1}\,x+{\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/8*(2-4*x)*_C2*ln(-1+2*x)+1/8*(4*x^2-2*x-1)*_C2-2*_C1*x+_C1