2.1358   ODE No. 1358

\[ y''(x)=\frac {\left (x^2-2\right ) y'(x)}{x \left (x^2-1\right )}-\frac {\left (x^2-2\right ) y(x)}{x^2 \left (x^2-1\right )} \]

✓ Mathematica : cpu = 0.0315657 (sec), leaf count = 66

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]
 

\[\left \{\left \{y(x)\to \frac {c_1 x \sqrt [4]{x^2-1}}{\sqrt [4]{1-x^2}}+\frac {c_2 x \sqrt [4]{x^2-1} \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )}{\sqrt [4]{1-x^2}}\right \}\right \}\]

✓ Maple : cpu = 0.074 (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))
 

\[y \left (x \right ) = x \left (\ln \left (x +\sqrt {x^{2}-1}\right ) c_{2} +c_{1} \right )\]