4.56   ODE No. 1056

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

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

Mathematica: cpu = 0.036005 (sec), leaf count = 66 \[ \left \{\left \{y(x)\to c_1 x-\frac {c_2 \left (3 e^{\frac {x^3}{3}} \left (-x^3\right )^{2/3}+3^{2/3} x^3 \Gamma \left (\frac {2}{3},-\frac {x^3}{3}\right )\right )}{3 \left (-x^3\right )^{2/3}}\right \}\right \} \]

Maple: cpu = 0.078 (sec), leaf count = 48 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\frac {{\it \_C2}}{{x}^{2}} \left ( \sqrt [3]{3}{{\rm e}^{{\frac {{x}^{3}}{3}}}} \left ( -{x}^{3} \right ) ^{{\frac {2}{3}}}-{x}^{3} \left ( \Gamma \left ( {\frac {2}{3} } \right ) -\Gamma \left ( {\frac {2}{3}},-{\frac {{x}^{3}}{3}} \right ) \right ) \right ) } \right \} \]