2.1024   ODE No. 1024

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

\[ y''(x)-y(x) \left (2 \tan ^2(x)+1\right )=0 \] Mathematica : cpu = 0.161789 (sec), leaf count = 54

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

Maple : cpu = 0.139 (sec), leaf count = 30

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