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 = 0.0219603 (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 = 0.021 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac {2\,\ln \left ( x \right ) {\it \_C2}\,x-{\it \_C2}\,{x}^{2}+{\it \_C1}\,x+{\it \_C2}}{-1+x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = (2*ln(x)*_C2*x-_C2*x^2+_C1*x+_C2)/(-1+x)