5.81   ODE No. 1529

\[ \boxed { \left ( \sin \left ( x \right ) +x \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +3\, \left ( \cos \left ( x \right ) +1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -3\,\sin \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \cos \left ( x \right ) +\sin \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.077010 (sec), leaf count = 42 \[ \text {DSolve}\left [y^{(3)}(x) (x+\sin (x))+3 (\cos (x)+1) y''(x)-3 \sin (x) y'(x)-y(x) \cos (x)+\sin (x)=0,y(x),x\right ] \]

Maple: cpu = 0.047 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{2}}{\sin \left ( x \right ) +x}}+{\frac {{\it \_C2}\,x}{\sin \left ( x \right ) +x}}-{ \frac {\cos \left ( x \right ) }{\sin \left ( x \right ) +x}}+{\frac {{ \it \_C3}}{\sin \left ( x \right ) +x}} \right \} \]