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 = 0.0601935 (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 = 0.013 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\frac {\ln \left ( x \right ) {\it \_C1}\,x+{\it \_C2}\,x+{\it \_C1}}{ \left ( -1+x \right ) ^{2}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = (ln(x)*_C1*x+_C2*x+_C1)/(-1+x)^2