ODE
\[ \left (1-x^2\right ) y''(x)-2 x y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.186007 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {1}{2} c_1 (\log (1-x)-\log (x+1))+c_2\right \}\right \}\]
Maple ✓
cpu = 0.057 (sec), leaf count = 21
\[\left [y \left (x \right ) = \textit {\_C1} +\left (-\frac {\ln \left (x +1\right )}{2}+\frac {\ln \left (x -1\right )}{2}\right ) \textit {\_C2}\right ]\] Mathematica raw input
DSolve[-2*x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2] + (C[1]*(Log[1 - x] - Log[1 + x]))/2}}
Maple raw input
dsolve((-x^2+1)*diff(diff(y(x),x),x)-2*x*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = _C1+(-1/2*ln(x+1)+1/2*ln(x-1))*_C2]