ODE
\[ (1-x) x y''(x)-3 x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.188108 (sec), leaf count = 38
\[\left \{\left \{y(x)\to \frac {c_1 x-c_2 x \log (x)-c_2}{\sqrt {1-x} (x-1)^{3/2}}\right \}\right \}\]
Maple ✓
cpu = 0.07 (sec), leaf count = 23
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \left (\frac {1}{x}+\ln \left (x \right )\right )+\textit {\_C2}}{x -2+\frac {1}{x}}\right ]\] Mathematica raw input
DSolve[-y[x] - 3*x*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x*C[1] - C[2] - x*C[2]*Log[x])/(Sqrt[1 - x]*(-1 + x)^(3/2))}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-3*x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = (_C1*(1/x+ln(x))+_C2)/(x-2+1/x)]