3.352   ODE No. 352

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

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

Mathematica: cpu = 0.132017 (sec), leaf count = 43 \[ \text {Solve}\left [4 \sin (\alpha ) \sin (x) \sin (y(x))-4 \left (\frac {y(x)}{2}+\frac {1}{4} \sin (2 y(x))\right )-2 x-\sin (2 x)=c_1,y(x)\right ] \]

Maple: cpu = 0.188 (sec), leaf count = 35 \[ \left \{ -\sin \left ( x \right ) \sin \left ( \alpha \right ) \sin \left ( y \left ( x \right ) \right ) +{\frac {\cos \left ( x \right ) \sin \left ( x \right ) }{2}}+{\frac {x}{2}}+{\frac {\sin \left ( y \left ( x \right ) \right ) \cos \left ( y \left ( x \right ) \right ) }{2 }}+{\frac {y \left ( x \right ) }{2}}+{\it \_C1}=0 \right \} \]