4.309   ODE No. 1309

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

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

Mathematica: cpu = 0.081010 (sec), leaf count = 84 \[ \left \{\left \{y(x)\to c_2 G_{1,2}^{2,0}\left (-\frac {1}{2 x^2}| \begin {array}{c} 1 \\ -\frac {1}{2},-\frac {1}{2} \\ \end {array} \right )+\sqrt {2} c_1 e^{\frac {1}{4 x^2}} x \left (\left (1-\frac {1}{2 x^2}\right ) I_0\left (\frac {1}{4 x^2}\right )+\frac {I_1\left (\frac {1}{4 x^2}\right )}{2 x^2}\right )\right \}\right \} \]

Maple: cpu = 0.078 (sec), leaf count = 73 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{x}{{\rm e}^{{\frac {1 }{4\,{x}^{2}}}}} \left ( \left ( 2\,{x}^{2}-1 \right ) {{\sl I}_{0 }\left ({\frac {1}{4\,{x}^{2}}}\right )}+{{\sl I}_{1}\left ({\frac {1}{4 \,{x}^{2}}}\right )} \right ) }+{\frac {{\it \_C2}}{x}{{\rm e}^{{\frac { 1}{4\,{x}^{2}}}}} \left ( \left ( 2\,{x}^{2}-1 \right ) {{\sl K}_{0 }\left (-{\frac {1}{4\,{x}^{2}}}\right )}+{{\sl K}_{1}\left (-{\frac {1}{ 4\,{x}^{2}}}\right )} \right ) } \right \} \]