3.349   ODE No. 349

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

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

Mathematica: cpu = 0.039005 (sec), leaf count = 15 \[ \left \{\left \{y(x)\to x \csc ^{-1}\left (2 \left (c_1+\log (x)\right )\right )\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 15 \[ \left \{ y \left ( x \right ) =\arcsin \left ( {\frac {1}{2\,\ln \left ( x \right ) +2\,{\it \_C1}}} \right ) x \right \} \]