2.1309   ODE No. 1309

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

\[ x^3 y''(x)-\left (x^2-1\right ) y'(x)+x y(x)=0 \] Mathematica : cpu = 0.0999429 (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 = 0.148 (sec), leaf count = 85

\[\left \{y \left (x \right ) = \frac {c_{1} \left (2 x^{2} \BesselI \left (0, \frac {1}{4 x^{2}}\right )-\BesselI \left (0, \frac {1}{4 x^{2}}\right )+\BesselI \left (1, \frac {1}{4 x^{2}}\right )\right ) {\mathrm e}^{\frac {1}{4 x^{2}}}}{x}+\frac {c_{2} \left (2 x^{2} \BesselK \left (0, -\frac {1}{4 x^{2}}\right )-\BesselK \left (0, -\frac {1}{4 x^{2}}\right )+\BesselK \left (1, -\frac {1}{4 x^{2}}\right )\right ) {\mathrm e}^{\frac {1}{4 x^{2}}}}{x}\right \}\]