2.1309   ODE No. 1309

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

\[ -\left (x^2-1\right ) y'(x)+x^3 y''(x)+x y(x)=0 \] Mathematica : cpu = 0.0947751 (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 = 0.271 (sec), leaf count = 85

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{x}{{\rm e}^{{\frac {1}{4\,{x}^{2}}}}} \left ( 2\,{{\sl I}_{0}\left (1/4\,{x}^{-2}\right )}{x}^{2}-{{\sl I}_{0}\left ({\frac {1}{4\,{x}^{2}}}\right )}+{{\sl I}_{1}\left ({\frac {1}{4\,{x}^{2}}}\right )} \right ) }+{\frac {{\it \_C2}}{x}{{\rm e}^{{\frac {1}{4\,{x}^{2}}}}} \left ( 2\,{{\sl K}_{0}\left (-1/4\,{x}^{-2}\right )}{x}^{2}-{{\sl K}_{0}\left (-{\frac {1}{4\,{x}^{2}}}\right )}+{{\sl K}_{1}\left (-{\frac {1}{4\,{x}^{2}}}\right )} \right ) } \right \} \]