2.22   ODE No. 22

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

\[ y'(x)-y(x)^2-y(x) \sin (2 x)-\cos (2 x)=0 \] Mathematica : cpu = 0 (sec), leaf count = 0 , crash

Kernel Crash

Maple : cpu = 0.372 (sec), leaf count = 198

\[ \left \{ y \left ( x \right ) = \left ( 2\,{\frac {{\it \_C1}\,\cos \left ( 2\,x \right ) }{\sqrt {2\,\cos \left ( 2\,x \right ) +2}}{\it HeunCPrime} \left ( 1,1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left ( 2\,x \right ) +1/2 \right ) \left ( {\it \_C1}\,{\it HeunC} \left ( 1,1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left ( 2\,x \right ) +1/2 \right ) \sqrt {2\,\cos \left ( 2\,x \right ) +2}+{\it HeunC} \left ( 1,-1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left ( 2\,x \right ) +1/2 \right ) \right ) ^{-1}}+{1 \left ( {\it HeunCPrime} \left ( 1,-{\frac {1}{2}},-{\frac {1}{2}},-1,{\frac {7}{8}},{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}} \right ) \sqrt {2\,\cos \left ( 2\,x \right ) +2}+2\,{\it HeunCPrime} \left ( 1,1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left ( 2\,x \right ) +1/2 \right ) {\it \_C1}+2\,{\it HeunC} \left ( 1,1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left ( 2\,x \right ) +1/2 \right ) {\it \_C1} \right ) {\frac {1}{\sqrt {2\,\cos \left ( 2\,x \right ) +2}}} \left ( {\it \_C1}\,{\it HeunC} \left ( 1,{\frac {1}{2}},-{\frac {1}{2}},-1,{\frac {7}{8}},{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}} \right ) \sqrt {2\,\cos \left ( 2\,x \right ) +2}+{\it HeunC} \left ( 1,-{\frac {1}{2}},-{\frac {1}{2}},-1,{\frac {7}{8}},{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}} \right ) \right ) ^{-1}} \right ) \sin \left ( 2\,x \right ) \right \} \]