ODE No. 1059

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

\[ x^4 y'(x)-x^3 y(x)+y''(x)=0 \] Mathematica : cpu = 0.069901 (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 = 0.131 (sec), leaf count = 56

\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{7}} \left ( 9\,{\it \_C2}\,{{\rm e}^{-1/10\,{x}^{5}}} \left ( {x}^{5}+4 \right ) {{\sl M}_{7/5,\,{\frac {9}{10}}}\left (1/5\,{x}^{5}\right )}+{x}^{8} \left ( {x}^{2}{\it \_C2}\,{{\rm e}^{-{\frac {{x}^{5}}{10}}}}{{\sl M}_{{\frac {2}{5}},\,{\frac {9}{10}}}\left ({\frac {{x}^{5}}{5}}\right )}+{\it \_C1} \right ) \right ) } \right \} \]