2.1151   ODE No. 1151

\[ \left (-a x^2-2\right ) y(x)+x^2 y''(x)=0 \] Mathematica : cpu = 0.0112511 (sec), leaf count = 129


\[\left \{\left \{y(x)\to \frac {\sqrt {\frac {2}{\pi }} c_2 \sqrt {x} \left (i \sinh \left (\sqrt {a} x\right )-\frac {i \cosh \left (\sqrt {a} x\right )}{\sqrt {a} x}\right )}{\sqrt {-i \sqrt {a} x}}+\frac {\sqrt {\frac {2}{\pi }} c_1 \sqrt {x} \left (\frac {\sinh \left (\sqrt {a} x\right )}{\sqrt {a} x}-\cosh \left (\sqrt {a} x\right )\right )}{\sqrt {-i \sqrt {a} x}}\right \}\right \}\] Maple : cpu = 0.089 (sec), leaf count = 43


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