ODE
\[ (1-x) x y''(x)+2 y'(x)+6 y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0525542 (sec), leaf count = 90
\[\left \{\left \{y(x)\to \frac {-3 c_1 x^4+9 c_1 x^3+12 c_2 x^3-9 c_1 x^2-30 c_2 x^2+3 c_1 x+22 c_2 x+12 c_2 (x-1)^3 x \log (1-x)-12 c_2 (x-1)^3 x \log (x)-3 c_2}{3 x}\right \}\right \}\]
Maple ✓
cpu = 0.042 (sec), leaf count = 54
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( -1+x \right ) ^{3}+12\,{\frac {{\it \_C2}}{x} \left ( -x \left ( -1+x \right ) ^{3}\ln \left ( -1+x \right ) +x \left ( -1+x \right ) ^{3}\ln \left ( x \right ) -{x}^{3}+5/2\,{x}^{2}-{\frac {11\,x}{6}}+1/4 \right ) } \right \} \] Mathematica raw input
DSolve[6*y[x] + 2*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (3*x*C[1] - 9*x^2*C[1] + 9*x^3*C[1] - 3*x^4*C[1] - 3*C[2] + 22*x*C[2] - 30*x^2*C[2] + 12*x^3*C[2] + 12*(-1 + x)^3*x*C[2]*Log[1 - x] - 12*(-1 + x)^3*x*C[2]*Log[x])/(3*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) = _C1*(-1+x)^3+12*_C2*(-x*(-1+x)^3*ln(-1+x)+x*(-1+x)^3*ln(x)-x^3+5/2*x^2-11/6*x+1/4)/x