4.417   ODE No. 1417

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

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

Mathematica: cpu = 0.141518 (sec), leaf count = 52 \[ \left \{\left \{y(x)\to c_1 e^{\frac {\cos (x)}{2}} \cos \left (\frac {1}{2} \sqrt {3} \cos (x)\right )+c_2 e^{\frac {\cos (x)}{2}} \sin \left (\frac {1}{2} \sqrt {3} \cos (x)\right )\right \}\right \} \]

Maple: cpu = 0.094 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {\cos \left ( x \right ) }{2}}}}\sin \left ( {\frac {\sqrt {3}\cos \left ( x \right ) }{2}} \right ) +{\it \_C2}\,{{\rm e}^{{\frac {\cos \left ( x \right ) }{2}}}}\cos \left ( {\frac {\sqrt {3}\cos \left ( x \right ) }{2 }} \right ) \right \} \]