2.1088   ODE No. 1088

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

\[ 4 y''(x)+4 \tan (x) y'(x)+y(x) \left (-\left (5 \tan ^2(x)+2\right )\right )=0 \] Mathematica : cpu = 0.102603 (sec), leaf count = 97

\[\left \{\left \{y(x)\to \frac {3 \sqrt [8]{-1} c_2 \sqrt [4]{-\cos ^4(x)} \sqrt {1+i \sqrt {-\cos ^4(x)}}+3 (-1)^{7/8} c_2 \sinh ^{-1}\left (\frac {(1+i) \sqrt [4]{-\cos ^4(x)}}{\sqrt {2}}\right )-2 (-1)^{7/8} c_1}{2 \sqrt [8]{-\cos ^4(x)}}\right \}\right \}\]

Maple : cpu = 0.14 (sec), leaf count = 31

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