3.364   ODE No. 364

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

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

Mathematica: cpu = 0.064008 (sec), leaf count = 31 \[ \text {Solve}\left [-\log \left (\frac {y(x)}{x}\right )-\log \left (\cos \left (\frac {y(x)}{x}\right )\right )=c_1+2 \log (x),y(x)\right ] \]

Maple: cpu = 0.078 (sec), leaf count = 23 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{\cos \left ( {\it RootOf} \left ( -{\it \_Z}\,{x}^{2}\cos \left ( {\it \_Z} \right ) +{\it \_C1} \right ) \right ) x}} \right \} \]