3.911   ODE No. 911

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =- \left ( -{\frac {\ln \left ( y \left ( x \right ) \right ) }{x}}+{\frac {\cos \left ( x \right ) \ln \left ( y \left ( x \right ) \right ) }{\sin \left ( x \right ) }}-{\it \_F1} \left ( x \right ) \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 4.337551 (sec), leaf count = 56 \[ \text {Solve}\left [\int _1^x \left (\frac {2 \log (y(x)) \sin (K[1])}{K[1]^2}-\frac {2 (\log (y(x)) \cos (K[1])-\sin (K[1]) \text {$\_$F1}(K[1]))}{K[1]}\right ) \, dK[1]-2 \sin (1) \log (y(x))=c_1,y(x)\right ] \]

Maple: cpu = 0.374 (sec), leaf count = 30 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {x{\it \_C1}}{\sin \left ( x \right ) }}}}{{\rm e}^{{\frac {x}{\sin \left ( x \right ) } \int \!{\frac {{\it \_F1} \left ( x \right ) \sin \left ( x \right ) }{x}} \,{\rm d}x}}} \right \} \]