4.397   ODE No. 1397

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{4}}}+{\frac {y \left ( x \right ) }{{x}^{5}}}=0} \]

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

Mathematica: cpu = 0.027003 (sec), leaf count = 38 \[ \left \{\left \{y(x)\to \frac {c_2 \Gamma \left (\frac {1}{3},-\frac {1}{3 x^3}\right )}{3^{2/3} \sqrt [3]{-\frac {1}{x^3}}}+c_1 x\right \}\right \} \]

Maple: cpu = 0.063 (sec), leaf count = 28 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\it \_C2}\, \left ( \pi \, \sqrt {3}-{\frac {3\,\Gamma \left ( 2/3 \right ) }{2}\Gamma \left ( { \frac {1}{3}},-{\frac {1}{3\,{x}^{3}}} \right ) } \right ) x \right \} \]