ODE
\[ a+\left (1-x^2\right ) y''(x)-2 x y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.187675 (sec), leaf count = 36
\[\left \{\left \{y(x)\to \frac {1}{2} (a+c_1) \log (1-x)+\frac {1}{2} (a-c_1) \log (x+1)+c_2\right \}\right \}\]
Maple ✓
cpu = 0.138 (sec), leaf count = 34
\[\left [y \left (x \right ) = \frac {\ln \left (x -1\right ) \textit {\_C1}}{2}+\frac {\ln \left (x -1\right ) a}{2}-\frac {\ln \left (x +1\right ) \textit {\_C1}}{2}+\frac {a \ln \left (x +1\right )}{2}+\textit {\_C2}\right ]\] Mathematica raw input
DSolve[a - 2*x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2] + ((a + C[1])*Log[1 - x])/2 + ((a - C[1])*Log[1 + x])/2}}
Maple raw input
dsolve((-x^2+1)*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+a = 0, y(x))
Maple raw output
[y(x) = 1/2*ln(x-1)*_C1+1/2*ln(x-1)*a-1/2*ln(x+1)*_C1+1/2*a*ln(x+1)+_C2]