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 = 0.0114869 (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 = 0.009 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\frac { \left ( \ln \left ( -1+x \right ) -\ln \left ( 1+x \right ) \right ) {\it \_C2}}{2}} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1+1/2*(ln(-1+x)-ln(1+x))*_C2