2.1200   ODE No. 1200

\[ (1-v) v y(x)+x^2 y''(x)+2 x^2 y'(x)=0 \] Mathematica : cpu = 0.0148909 (sec), leaf count = 62


\[\left \{\left \{y(x)\to c_1 e^{-x} \sqrt {x} J_{\frac {1}{2} (2 v-1)}(-i x)+c_2 e^{-x} \sqrt {x} Y_{\frac {1}{2} (2 v-1)}(-i x)\right \}\right \}\] Maple : cpu = 0.015 (sec), leaf count = 27


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