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 = 0.157514 (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 = 0.066 (sec), leaf count = 52
\[[y \left (x \right ) = \textit {\_C1} \left (6 x^{2}-6 x +1\right )+\textit {\_C2} \left (\left (6 x^{2}-6 x +1\right ) \ln \left (x \right )+\left (-6 x^{2}+6 x -1\right ) \ln \left (x -1\right )-6 x +3\right )]\] 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))
Maple raw output
[y(x) = _C1*(6*x^2-6*x+1)+_C2*((6*x^2-6*x+1)*ln(x)+(-6*x^2+6*x-1)*ln(x-1)-6*x+3)]