ODE
\[ x \left (1-x^2\right ) y''(x)-2 \left (1-x^2\right ) y'(x)-2 x y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.190544 (sec), leaf count = 48
\[\left \{\left \{y(x)\to -\left (c_1 \left (x^2-1\right )\right )-\frac {1}{4} c_2 \left (\left (x^2-1\right ) \log (1-x)-\left (x^2-1\right ) \log (x+1)-2 x\right )\right \}\right \}\]
Maple ✓
cpu = 0.048 (sec), leaf count = 41
\[\left [y \left (x \right ) = \left (\left (-\frac {1}{4 \left (x +1\right )}-\frac {\ln \left (x +1\right )}{4}-\frac {1}{4 \left (x -1\right )}+\frac {\ln \left (x -1\right )}{4}\right ) \textit {\_C1} +\textit {\_C2} \right ) \left (x^{2}-1\right )\right ]\] Mathematica raw input
DSolve[-2*x*y[x] - 2*(1 - x^2)*y'[x] + x*(1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((-1 + x^2)*C[1]) - (C[2]*(-2*x + (-1 + x^2)*Log[1 - x] - (-1 + x^2)*Log[1 + x]))/4}}
Maple raw input
dsolve(x*(-x^2+1)*diff(diff(y(x),x),x)-2*(-x^2+1)*diff(y(x),x)-2*x*y(x) = 0, y(x))
Maple raw output
[y(x) = ((-1/4/(x+1)-1/4*ln(x+1)-1/4/(x-1)+1/4*ln(x-1))*_C1+_C2)*(x^2-1)]