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 = 0.0187877 (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 = 0.019 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) =-2\,\ln \left ( x \right ) {\it \_C2}\,x+{\it \_C2}\,{x}^{2}+{\it \_C1}\,x-{\it \_C2} \right \} \] 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),'implicit')
Maple raw output
y(x) = -2*ln(x)*_C2*x+_C2*x^2+_C1*x-_C2