4.419   ODE No. 1419

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

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

Mathematica: cpu = 1.177650 (sec), leaf count = 53 \[ \text {DSolve}\left [y''(x)=-\frac {\sec (x) y'(x) \left (x^2 \sin (x)-2 x \cos (x)\right )}{x^2}-\frac {y(x) \sec (x) (2 x \cos (x)-x \sin (x))}{x^2},y(x),x\right ] \]

Maple: cpu = 0.219 (sec), leaf count = 13 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\it \_C2}\,x\sin \left ( x \right ) \right \} \]