\[ y''(x)=\frac {\left (x^2-2\right ) y'(x)}{x \left (x^2-1\right )}-\frac {\left (x^2-2\right ) y(x)}{x^2 \left (x^2-1\right )} \] ✓ Mathematica : cpu = 0.0420857 (sec), leaf count = 89
DSolve[Derivative[2][y][x] == -(((-2 + x^2)*y[x])/(x^2*(-1 + x^2))) + ((-2 + x^2)*Derivative[1][y][x])/(x*(-1 + x^2)),y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 x \sqrt [4]{x^2-1}}{\sqrt [4]{1-x^2}}-\frac {c_2 x \sqrt [4]{x^2-1} \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )\right )}{2 \sqrt [4]{1-x^2}}\right \}\right \}\] ✓ Maple : cpu = 0.043 (sec), leaf count = 20
dsolve(diff(diff(y(x),x),x) = 1/x*(x^2-2)/(x^2-1)*diff(y(x),x)-(x^2-2)/x^2/(x^2-1)*y(x),y(x))
\[y \left (x \right ) = x \left (\ln \left (x +\sqrt {x^{2}-1}\right ) c_{2}+c_{1}\right )\]