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 = 0.0499561 (sec), leaf count = 89

\[\left \{\left \{y(x)\to \frac {c_1 x \sqrt [4]{x^2-1}}{\sqrt [4]{1-x^2}}-\frac {c_2 x \sqrt [4]{x^2-1} \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )\right )}{2 \sqrt [4]{1-x^2}}\right \}\right \}\] Maple : cpu = 0.116 (sec), leaf count = 20

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