ODE
\[ (1-x)^2 x y''(x)-2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.171167 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {-c_2 x^2-c_1 x+2 c_2 x \log (x)+c_2}{x-1}\right \}\right \}\]
Maple ✓
cpu = 0.06 (sec), leaf count = 32
\[\left [y \left (x \right ) = \frac {\textit {\_C1} x}{x -1}+\frac {\textit {\_C2} \left (2 x \ln \left (x \right )-x^{2}+1\right )}{x -1}\right ]\] Mathematica raw input
DSolve[-2*y[x] + (1 - x)^2*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-(x*C[1]) + C[2] - x^2*C[2] + 2*x*C[2]*Log[x])/(-1 + x)}}
Maple raw input
dsolve(x*(1-x)^2*diff(diff(y(x),x),x)-2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x/(x-1)+_C2/(x-1)*(2*x*ln(x)-x^2+1)]