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 = 0.176377 (sec), leaf count = 21
\[\left \{\left \{y(x)\to -\frac {x (c_2 \log (x)+c_1)}{x-1}\right \}\right \}\]
Maple ✓
cpu = 0.054 (sec), leaf count = 23
\[\left [y \left (x \right ) = \frac {\textit {\_C1} x}{x -1}+\frac {\textit {\_C2} x \ln \left (x \right )}{x -1}\right ]\] 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*(x+1)*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x/(x-1)+_C2*x/(x-1)*ln(x)]