ODE
\[ (1-x) x y''(x)-2 y'(x)+6 y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0482478 (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 = 0.044 (sec), leaf count = 62
\[ \left \{ y \left ( x \right ) ={\frac {-12\,{\it \_C2}\,{x}^{3} \left ( -1+x \right ) \ln \left ( -1+x \right ) +12\,{\it \_C2}\,{x}^{3} \left ( -1+x \right ) \ln \left ( x \right ) +{\it \_C1}\,{x}^{4}+ \left ( -{\it \_C1}-12\,{\it \_C2} \right ) {x}^{3}+6\,{\it \_C2}\,{x}^{2}+2\,{\it \_C2}\,x+{\it \_C2}}{-1+x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = (-12*_C2*x^3*(-1+x)*ln(-1+x)+12*_C2*x^3*(-1+x)*ln(x)+_C1*x^4+(-_C1-12*_C2)*x^3+6*_C2*x^2+2*_C2*x+_C2)/(-1+x)