2.1422   ODE No. 1422

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

\[ y''(x)=2 y(x) \csc ^2(x) \] Mathematica : cpu = 0.097039 (sec), leaf count = 43

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

Maple : cpu = 0.265 (sec), leaf count = 50

\[ \left \{ y \left ( x \right ) ={\frac {-i\sin \left ( 2\,x \right ) \ln \left ( \cos \left ( 2\,x \right ) +i\sin \left ( 2\,x \right ) \right ) {\it \_C2}+{\it \_C1}\,\sin \left ( 2\,x \right ) +2\,{\it \_C2}\, \left ( \cos \left ( 2\,x \right ) -1 \right ) }{\cos \left ( 2\,x \right ) -1}} \right \} \]