2.1385   ODE No. 1385

\[ y''(x)=-\frac {\left (a x^2+a-3\right ) y(x)}{4 \left (x^2+1\right )^2} \] Mathematica : cpu = 0.0129023 (sec), leaf count = 78


\[\left \{\left \{y(x)\to c_1 \sqrt {x^2+1} P_{\frac {1}{2} \left (\sqrt {1-a}-1\right )}^{\frac {1}{2}}(i x)+c_2 \sqrt {x^2+1} Q_{\frac {1}{2} \left (\sqrt {1-a}-1\right )}^{\frac {1}{2}}(i x)\right \}\right \}\] Maple : cpu = 0.058 (sec), leaf count = 55


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