4.307   ODE No. 1307

\[ \boxed { {x}^{3}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +x \left ( 1+x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.085011 (sec), leaf count = 54 \[ \left \{\left \{y(x)\to \frac {c_1 e^{\frac {1}{x}} (x+1)}{x}-\frac {c_2 \left (e^{\frac {1}{x}} x \text {Ei}\left (-\frac {1}{x}\right )+e^{\frac {1}{x}} \text {Ei}\left (-\frac {1}{x}\right )+x\right )}{x}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 38 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{{\rm e}^{{x}^{-1}}} \left ( 1+x \right ) }{x}}+{\frac {{\it \_C2}\, \left ( -{{\rm e}^{{x}^{ -1}}} \left ( 1+x \right ) {\it Ei} \left ( 1,{x}^{-1} \right ) +x \right ) }{x}} \right \} \]