ODE
\[ \left (1-x^2\right ) x^2 y''(x)-\left (2-x^2\right ) x y'(x)+\left (2-x^2\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0587328 (sec), leaf count = 45
\[\left \{\left \{y(x)\to \frac {x \sqrt [4]{x^2-1} \left (c_2 \log \left (\sqrt {x^2-1}+x\right )+c_1\right )}{\sqrt [4]{1-x^2}}\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) =x \left ( \ln \left ( x+\sqrt {{x}^{2}-1} \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[(2 - x^2)*y[x] - x*(2 - x^2)*y'[x] + x^2*(1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x*(-1 + x^2)^(1/4)*(C[1] + C[2]*Log[x + Sqrt[-1 + x^2]]))/(1 - x^2)^(1/4)}}
Maple raw input
dsolve(x^2*(-x^2+1)*diff(diff(y(x),x),x)-x*(-x^2+2)*diff(y(x),x)+(-x^2+2)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x*(ln(x+(x^2-1)^(1/2))*_C2+_C1)