2.1405   ODE No. 1405

\[ y''(x)=\frac {\left (2 x^2+1\right ) y'(x)}{x^3}-\frac {\left (a x^4+10 x^2+1\right ) y(x)}{4 x^6} \] Mathematica : cpu = 0.0478268 (sec), leaf count = 77


\[\left \{\left \{y(x)\to c_1 e^{-\frac {1}{4 x^2}} x^{\frac {3}{2}-\frac {\sqrt {9-a}}{2}}+\frac {c_2 e^{-\frac {1}{4 x^2}} x^{\frac {\sqrt {9-a}}{2}+\frac {3}{2}}}{\sqrt {9-a}}\right \}\right \}\] Maple : cpu = 0.065 (sec), leaf count = 42


\[y \relax (x ) = {\mathrm e}^{-\frac {1}{4 x^{2}}} \left (x^{\frac {3}{2}-\frac {\sqrt {-a +9}}{2}} c_{2}+x^{\frac {3}{2}+\frac {\sqrt {-a +9}}{2}} c_{1}\right )\]