ODE
\[ (1-x) x y''(x)+(1-4 x) y'(x)-2 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.022975 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {-c_2 x+c_2 \log (x)+c_1}{(x-1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,\ln \left ( x \right ) -{\it \_C1}\,x+{\it \_C2}}{ \left ( -1+x \right ) ^{2}}} \right \} \] Mathematica raw input
DSolve[-2*y[x] + (1 - 4*x)*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] - x*C[2] + C[2]*Log[x])/(-1 + x)^2}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)+(1-4*x)*diff(y(x),x)-2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1*ln(x)-_C1*x+_C2)/(-1+x)^2