2.1309   ODE No. 1309

\[ x^3 y''(x)-\left (x^2-1\right ) y'(x)+x y(x)=0 \] Mathematica : cpu = 0.086244 (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 = 0.089 (sec), leaf count = 85


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