ODE
\[ \left (1-x^2\right ) y''(x)+x y'(x)-y(x)=0 \] ODE Classification
[_Gegenbauer]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0309846 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -c_2 \sqrt {x^2-1}+c_2 x \log \left (\sqrt {x^2-1}+x\right )+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) = \left ( \ln \left ( x+\sqrt {{x}^{2}-1} \right ) {\it \_C2}+{\it \_C1} \right ) x-\sqrt {{x}^{2}-1}{\it \_C2} \right \} \] Mathematica raw input
DSolve[-y[x] + x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] - Sqrt[-1 + x^2]*C[2] + x*C[2]*Log[x + Sqrt[-1 + x^2]]}}
Maple raw input
dsolve((-x^2+1)*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (ln(x+(x^2-1)^(1/2))*_C2+_C1)*x-(x^2-1)^(1/2)*_C2