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 = 0.173682 (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 = 0.046 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {\left (-x +\ln \left (x \right )\right ) \textit {\_C1}}{\left (x -1\right )^{2}}+\frac {\textit {\_C2}}{\left (x -1\right )^{2}}\right ]\] 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))
Maple raw output
[y(x) = (-x+ln(x))/(x-1)^2*_C1+_C2/(x-1)^2]