4.88   ODE No. 1088

\[ \boxed { 4\,{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +4\, \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \tan \left ( x \right ) - \left ( 5\, \left ( \tan \left ( x \right ) \right ) ^{2}+2 \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.102513 (sec), leaf count = 180 \[ \left \{\left \{y(x)\to -\frac {(-1)^{7/8} 2^{5/8} c_1}{\sqrt [8]{-8 \cos ^2(2 x)-16 \cos (2 x)-8}}+\frac {3 (-1)^{5/8} c_2 \left (4 \sqrt [4]{-1} 2^{3/4} \sinh ^{-1}\left (\frac {1}{2} \sqrt [4]{-\frac {1}{2}} \sqrt [4]{-8 \cos ^2(2 x)-16 \cos (2 x)-8}\right )-i \sqrt [4]{-8 \cos ^2(2 x)-16 \cos (2 x)-8} \sqrt {8+i \sqrt {2} \sqrt {-8 \cos ^2(2 x)-16 \cos (2 x)-8}}\right )}{8 \sqrt [8]{2} \sqrt [8]{-8 \cos ^2(2 x)-16 \cos (2 x)-8}}\right \}\right \} \]

Maple: cpu = 0.094 (sec), leaf count = 36 \[ \left \{ y \left ( x \right ) ={{\it \_C1}{\frac {1}{\sqrt {\cos \left ( x \right ) }}}}+{{\it \_C2}\, \left ( i\cos \left ( x \right ) \sin \left ( x \right ) -\ln \left ( \sin \left ( x \right ) +i\cos \left ( x \right ) \right ) \right ) {\frac {1}{\sqrt {\cos \left ( x \right ) }}} } \right \} \]