2.1114   ODE No. 1114

\[ x y''(x)-2 (x-1) y'(x)-y(x)=0 \] Mathematica : cpu = 0.0386883 (sec), leaf count = 39


\[\left \{\left \{y(x)\to c_2 G_{1,2}^{2,0}\left (-2 x\left |\begin {array}{c} \frac {1}{2} \\ -1,0 \\\end {array}\right .\right )+c_1 e^x (I_0(x)-I_1(x))\right \}\right \}\] Maple : cpu = 0.049 (sec), leaf count = 34


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