2.904   ODE No. 904

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

\[ y'(x)=\frac {\sin \left (\frac {y(x)}{x}\right ) \csc \left (\frac {y(x)}{2 x}\right ) \sec \left (\frac {y(x)}{2 x}\right ) \left (2 x^3 \sin \left (\frac {y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+y(x)\right )}{2 x} \] Mathematica : cpu = 0.0955035 (sec), leaf count = 23

\[\left \{\left \{y(x)\to 2 x \cot ^{-1}\left (e^{-\frac {x^2}{2}-c_1}\right )\right \}\right \}\] Maple : cpu = 0.203 (sec), leaf count = 64

\[ \left \{ y \left ( x \right ) =\arctan \left ( 2\,{\frac {{{\rm e}^{1/2\,{x}^{2}}}{\it \_C1}}{{{\it \_C1}}^{2} \left ( {{\rm e}^{1/2\,{x}^{2}}} \right ) ^{2}+1}},{ \left ( -{{\it \_C1}}^{2} \left ( {{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) ^{2}+1 \right ) \left ( {{\it \_C1}}^{2} \left ( {{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) ^{2}+1 \right ) ^{-1}} \right ) x \right \} \]