ODE
\[ (1-x) x y''(x)+2 x y'(x)-2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.165257 (sec), leaf count = 26
\[\left \{\left \{y(x)\to c_2 \left (-x^2+2 x \log (x)+1\right )-c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.065 (sec), leaf count = 20
\[[y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \left (-2 x \ln \left (x \right )+x^{2}-1\right )]\] Mathematica raw input
DSolve[-2*y[x] + 2*x*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(x*C[1]) + C[2]*(1 - x^2 + 2*x*Log[x])}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x+_C2*(-2*x*ln(x)+x^2-1)]