5.22   ODE No. 1470

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

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

Mathematica: cpu = 75.667609 (sec), leaf count = 63 \[ \left \{\left \{y(x)\to e^{-\cos (x)} \int _1^x \frac {1}{4} e^{\cos (K[1])} \left (4 c_1 K[1]-3 K[1]^2+2 K[1]^2 \log (K[1])+4 c_2\right ) \, dK[1]+c_3 e^{-\cos (x)}\right \}\right \} \]

Maple: cpu = 0.062 (sec), leaf count = 36 \[ \left \{ y \left ( x \right ) = \left ( {\it \_C3}+\int \! \left ( 2\,x{ \it \_C1}+{\it \_C2}+{\frac {{x}^{2}\ln \left ( x \right ) }{2}}-{ \frac {3\,{x}^{2}}{4}} \right ) {{\rm e}^{\cos \left ( x \right ) }} \,{\rm d}x \right ) {{\rm e}^{-\cos \left ( x \right ) }} \right \} \]