2.1358   ODE No. 1358

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y''(x)=\frac {\left (x^2-2\right ) y'(x)}{x \left (x^2-1\right )}-\frac {\left (x^2-2\right ) y(x)}{x^2 \left (x^2-1\right )} \] Mathematica : cpu = 0.0664978 (sec), leaf count = 66

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

Maple : cpu = 0.24 (sec), leaf count = 21

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,x+{\it \_C2}\,x\ln \left ( x+\sqrt {{x}^{2}-1} \right ) \right \} \]