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 = 0.0789975 (sec), leaf count = 36
\[\left \{\left \{y(x)\to \frac {1}{2} \left (a+c_1\right ) \log (1-x)+\frac {1}{2} \left (a-c_1\right ) \log (x+1)+c_2\right \}\right \}\]
Maple ✓
cpu = 0.024 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) ={\frac { \left ( a+{\it \_C1} \right ) \ln \left ( -1+x \right ) }{2}}+{\frac { \left ( a-{\it \_C1} \right ) \ln \left ( 1+x \right ) }{2}}+{\it \_C2} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/2*(a+_C1)*ln(-1+x)+1/2*(a-_C1)*ln(1+x)+_C2