ODE
\[ (1-x) x y''(x)-(x+1) y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0160223 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {c_2 x^2+2 c_1}{2-2 x}\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}{\it \_C2}+{\it \_C1}}{-1+x}} \right \} \] Mathematica raw input
DSolve[y[x] - (1 + x)*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*C[1] + x^2*C[2])/(2 - 2*x)}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-(1+x)*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*x^2+_C1)/(-1+x)