ODE
\[ (1-x) x y''(x)+2 y'(x)+6 y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.202836 (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 = 0.069 (sec), leaf count = 54
\[\left [y \left (x \right ) = \textit {\_C1} \left (x -1\right )^{3}+\frac {\textit {\_C2} \left (-12 x \left (x -1\right )^{3} \ln \left (x -1\right )+12 x \left (x -1\right )^{3} \ln \left (x \right )-12 x^{3}+30 x^{2}-22 x +3\right )}{x}\right ]\] Mathematica raw input
DSolve[6*y[x] + 2*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (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))
Maple raw output
[y(x) = _C1*(x-1)^3+_C2*(-12*x*(x-1)^3*ln(x-1)+12*x*(x-1)^3*ln(x)-12*x^3+30*x^2-22*x+3)/x]