ODE
\[ (1-x) x y''(x)+(1-2 x) y'(x)+6 y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0123803 (sec), leaf count = 56
\[\left \{\left \{y(x)\to c_1 \left (6 x^2-6 x+1\right )+c_2 \left (-\frac {1}{2} \left (6 x^2-6 x+1\right ) (\log (2-2 x)-\log (2 x))-3 x+\frac {3}{2}\right )\right \}\right \}\]
Maple ✓
cpu = 0.049 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) =-6\, \left ( {x}^{2}-x+1/6 \right ) {\it \_C2}\,\ln \left ( -1+x \right ) +6\, \left ( {x}^{2}-x+1/6 \right ) {\it \_C2}\,\ln \left ( x \right ) + \left ( -6\,x+3 \right ) {\it \_C2}+6\, \left ( {x}^{2}-x+1/6 \right ) {\it \_C1} \right \} \] Mathematica raw input
DSolve[6*y[x] + (1 - 2*x)*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 - 6*x + 6*x^2)*C[1] + C[2]*(3/2 - 3*x - ((1 - 6*x + 6*x^2)*(Log[2 - 2*x] - Log[2*x]))/2)}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)+(1-2*x)*diff(y(x),x)+6*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = -6*(x^2-x+1/6)*_C2*ln(-1+x)+6*(x^2-x+1/6)*_C2*ln(x)+(-6*x+3)*_C2+6*(x^2-x+1/6)*_C1