4.422   ODE No. 1422

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =2\,{\frac {y \left ( x \right ) }{ \left ( \sin \left ( x \right ) \right ) ^{2}}}=0} \]

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

Mathematica: cpu = 0.086011 (sec), leaf count = 64 \[ \left \{\left \{y(x)\to \frac {c_1 \cos (x)}{\sqrt {\cos ^2(x)-1}}+\frac {c_2 \left (\cos (x) \log \left (\sqrt {\cos ^2(x)-1}+\cos (x)\right )-\sqrt {\cos ^2(x)-1}\right )}{\sqrt {\cos ^2(x)-1}}\right \}\right \} \]

Maple: cpu = 0.156 (sec), leaf count = 57 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,\sin \left ( 2\,x \right ) }{\cos \left ( 2\,x \right ) -1}}+{\frac {{\it \_C2}\, \left ( - i\ln \left ( \cos \left ( 2\,x \right ) +i\sin \left ( 2\,x \right ) \right ) \sin \left ( 2\,x \right ) +2\,\cos \left ( 2\,x \right ) -2 \right ) }{\cos \left ( 2\,x \right ) -1}} \right \} \]