ODE
\[ (1-x) x y''(x)-2 y'(x)+6 y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.193778 (sec), leaf count = 62
\[\left \{\left \{y(x)\to c_1 x^3-\frac {c_2 \left (12 x^3+12 (x-1) x^3 \log (1-x)-12 (x-1) x^3 \log (x)-6 x^2-2 x-1\right )}{3 (x-1)}\right \}\right \}\]
Maple ✓
cpu = 0.069 (sec), leaf count = 62
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{3}+\frac {\textit {\_C2} \left (\left (12 x^{4}-12 x^{3}\right ) \ln \left (x \right )+\left (-12 x^{4}+12 x^{3}\right ) \ln \left (x -1\right )-12 x^{3}+6 x^{2}+2 x +1\right )}{x -1}\right ]\] Mathematica raw input
DSolve[6*y[x] - 2*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^3*C[1] - (C[2]*(-1 - 2*x - 6*x^2 + 12*x^3 + 12*(-1 + x)*x^3*Log[1 - x] - 12*(-1 + x)*x^3*Log[x]))/(3*(-1 + x))}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-2*diff(y(x),x)+6*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^3+_C2/(x-1)*((12*x^4-12*x^3)*ln(x)+(-12*x^4+12*x^3)*ln(x-1)-12*x^3+6*x^2+2*x+1)]