4.59   ODE No. 1059

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

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

Mathematica: cpu = 0.052007 (sec), leaf count = 72 \[ \left \{\left \{y(x)\to c_1 x-\frac {c_2 e^{-\frac {x^5}{5}} \left (5 \left (x^5\right )^{4/5}-5^{4/5} e^{\frac {x^5}{5}} x^5 \Gamma \left (\frac {4}{5},\frac {x^5}{5}\right )\right )}{5 \left (x^5\right )^{4/5}}\right \}\right \} \]

Maple: cpu = 0.062 (sec), leaf count = 55 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\frac {{\it \_C2}}{{x}^{7}}{ {\rm e}^{-{\frac {{x}^{5}}{10}}}} \left ( {x}^{10}{{\sl M}_{{\frac {2}{ 5}},\,{\frac {9}{10}}}\left ({\frac {{x}^{5}}{5}}\right )}+9\,{{\sl M}_{ 7/5,\,{\frac {9}{10}}}\left (1/5\,{x}^{5}\right )}{x}^{5}+36\,{{\sl M}_{ 7/5,\,{\frac {9}{10}}}\left (1/5\,{x}^{5}\right )} \right ) } \right \} \]