4.305   ODE No. 1305

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

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

Mathematica: cpu = 0.071009 (sec), leaf count = 47 \[ \left \{\left \{y(x)\to c_2 G_{1,2}^{2,0}\left (-\frac {2}{x}| \begin {array}{c} \frac {1}{2} \\ -1,0 \\ \end {array} \right )+c_1 e^{\frac {1}{x}} \left (I_0\left (\frac {1}{x}\right )-I_1\left (\frac {1}{x}\right )\right )\right \}\right \} \]

Maple: cpu = 0.046 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{x}^{-1}}} \left ( { {\sl I}_{0}\left ({x}^{-1}\right )}-{{\sl I}_{1}\left ({x}^{-1}\right )} \right ) +{\it \_C2}\,{{\rm e}^{{x}^{-1}}} \left ( {{\sl K}_{0}\left (-{ x}^{-1}\right )}-{{\sl K}_{1}\left (-{x}^{-1}\right )} \right ) \right \} \]