2.1056   ODE No. 1056

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

\[ x^2 \left (-y'(x)\right )+y''(x)+x y(x)=0 \] Mathematica : cpu = 0.0515459 (sec), leaf count = 51

\[\left \{\left \{y(x)\to -c_2 e^{\frac {x^3}{3}}+\frac {c_2 \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},-\frac {x^3}{3}\right )}{\sqrt [3]{3}}+c_1 x\right \}\right \}\]

Maple : cpu = 0.13 (sec), leaf count = 48

\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{2}} \left ( - \left ( -{x}^{3} \right ) ^{{\frac {2}{3}}}\sqrt [3]{3}{{\rm e}^{{\frac {{x}^{3}}{3}}}}{\it \_C2}+{x}^{3} \left ( {\it \_C2}\,\Gamma \left ( {\frac {2}{3}} \right ) -{\it \_C2}\,\Gamma \left ( {\frac {2}{3}},-{\frac {{x}^{3}}{3}} \right ) +{\it \_C1} \right ) \right ) } \right \} \]