4.404   ODE No. 1404

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( 2\,{x}^{2}+1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{3}}}-1/4\,{\frac { \left ( -2\,{x}^{2}+1 \right ) y \left ( x \right ) }{{x}^{6}}}=0} \]

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

Mathematica: cpu = 0.023003 (sec), leaf count = 33 \[ \left \{\left \{y(x)\to \frac {c_1 e^{\frac {1}{4 x^2}}}{x}+c_2 e^{\frac {1}{4 x^2}}\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 24 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {1}{4\,{x}^{ 2}}}}}+{\frac {{\it \_C2}}{x}{{\rm e}^{{\frac {1}{4\,{x}^{2}}}}}} \right \} \]