2.1197   ODE No. 1197

\[ (-a-x) y(x)+x^2 y''(x)-\left (x^2-2 x\right ) y'(x)=0 \] Mathematica : cpu = 0.0131615 (sec), leaf count = 78


\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} (x-\log (x))} J_{\frac {1}{2} \sqrt {4 a+1}}\left (-\frac {i x}{2}\right )+c_2 e^{\frac {1}{2} (x-\log (x))} Y_{\frac {1}{2} \sqrt {4 a+1}}\left (-\frac {i x}{2}\right )\right \}\right \}\] Maple : cpu = 0.043 (sec), leaf count = 43


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