ODE
\[ (1-x) x y''(x)-2 y'(x)+2 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0170453 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {c_2 x^3+3 c_1}{3-3 x}\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{3}{\it \_C2}+{\it \_C1}}{-1+x}} \right \} \] Mathematica raw input
DSolve[2*y[x] - 2*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (3*C[1] + x^3*C[2])/(3 - 3*x)}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-2*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*x^3+_C1)/(-1+x)