3.80   ODE No. 80

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +f \left ( x \right ) \sin \left ( y \left ( x \right ) \right ) + \left ( 1-{\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) \cos \left ( y \left ( x \right ) \right ) -{\frac {\rm d}{{\rm d}x}}f \left ( x \right ) -1=0} \]

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

Mathematica: cpu = 23.831526 (sec), leaf count = 36 \[ \text {DSolve}\left [\left (1-f'(x)\right ) \cos (y(x))-f'(x)+f(x) \sin (y(x))+y'(x)-1=0,y(x),x\right ] \]

Maple: cpu = 0.811 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) =2\,\arctan \left ( {\frac {-{{\rm e}^{ \int \!f \left ( x \right ) \,{\rm d}x}}+\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}xf \left ( x \right ) +{\it \_C1} \,f \left ( x \right ) }{{\it \_C1}+\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x}} \right ) \right \} \]