4.304   ODE No. 1304

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

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

Mathematica: cpu = 0.034004 (sec), leaf count = 50 \[ \left \{\left \{y(x)\to \frac {c_2 \left (e^{\frac {1}{x}} \text {Ei}\left (-\frac {1}{x}\right )+2 x^3-x^2+x\right )}{6 x}+\frac {c_1 e^{\frac {1}{x}}}{x}\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{{\rm e}^{{x}^{-1}}} }{x}}+{\frac {{\it \_C2}\, \left ( -2\,{x}^{3}+{{\rm e}^{{x}^{-1}}}{ \it Ei} \left ( 1,{x}^{-1} \right ) +{x}^{2}-x \right ) }{x}} \right \} \]