3.903   ODE No. 903

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {1}{x}\sin \left ( {\frac {y \left ( x \right ) }{x}} \right ) \left ( y \left ( x \right ) +2\,{x}^{2}\sin \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \right ) \left ( \sin \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \right ) ^{-1} \left ( \cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \right ) ^{-1}}=0} \]

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

Mathematica: cpu = 0.050006 (sec), leaf count = 19 \[ \left \{\left \{y(x)\to 2 x \cot ^{-1}\left (e^{-c_1-x}\right )\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 48 \[ \left \{ y \left ( x \right ) =\arctan \left ( 2\,{\frac {{\it \_C1}\,{ {\rm e}^{x}}}{{{\it \_C1}}^{2} \left ( {{\rm e}^{x}} \right ) ^{2}+1}},- {\frac {{{\it \_C1}}^{2} \left ( {{\rm e}^{x}} \right ) ^{2}-1}{{{\it \_C1}}^{2} \left ( {{\rm e}^{x}} \right ) ^{2}+1}} \right ) x \right \} \]