4.345   ODE No. 1345

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

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

Mathematica: cpu = 0.028504 (sec), leaf count = 52 \[ \left \{\left \{y(x)\to c_1 e^{\frac {1}{2 x^2}} x-\sqrt {\frac {\pi }{2}} c_2 e^{\frac {1}{2 x^2}} x \text {erf}\left (\frac {1}{\sqrt {2} x}\right )\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,x{{\rm e}^{{\frac {1}{2\,{x}^ {2}}}}}+{\it \_C2}\,x{{\rm e}^{{\frac {1}{2\,{x}^{2}}}}}{\it Erf} \left ( {\frac {\sqrt {2}}{2\,x}} \right ) \right \} \]