3.904   ODE No. 904

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {1}{x}\sin \left ( {\frac {y \left ( x \right ) }{x}} \right ) \left ( y \left ( x \right ) +2\,{x}^{3}\cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \sin \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \right ) \left ( \sin \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \right ) ^{-1} \left ( \cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \right ) ^{-1}}=0} \]

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

Mathematica: cpu = 0.051506 (sec), leaf count = 23 \[ \left \{\left \{y(x)\to 2 x \cot ^{-1}\left (e^{-c_1-\frac {x^2}{2}}\right )\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 64 \[ \left \{ y \left ( x \right ) =\arctan \left ( 2\,{\frac {{{\rm e}^{1/2\, {x}^{2}}}{\it \_C1}}{ \left ( {{\rm e}^{1/2\,{x}^{2}}} \right ) ^{2}{{ \it \_C1}}^{2}+1}},-{1 \left ( \left ( {{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) ^{2}{{\it \_C1}}^{2}-1 \right ) \left ( \left ( {{\rm e}^{{ \frac {{x}^{2}}{2}}}} \right ) ^{2}{{\it \_C1}}^{2}+1 \right ) ^{-1}} \right ) x \right \} \]