ODE
\[ (1-x) x^2 y''(x)-(x+1) x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0220989 (sec), leaf count = 21
\[\left \{\left \{y(x)\to -\frac {x \left (c_2 \log (x)+c_1\right )}{x-1}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\frac {x \left ( \ln \left ( x \right ) {\it \_C2}+{\it \_C1} \right ) }{-1+x}} \right \} \] Mathematica raw input
DSolve[y[x] - x*(1 + x)*y'[x] + (1 - x)*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((x*(C[1] + C[2]*Log[x]))/(-1 + x))}}
Maple raw input
dsolve(x^2*(1-x)*diff(diff(y(x),x),x)-x*(1+x)*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x*(ln(x)*_C2+_C1)/(-1+x)