2.1277   ODE No. 1277

\[ \left (-a x^2-1\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0 \] Mathematica : cpu = 0.0205306 (sec), leaf count = 51


\[\left \{\left \{y(x)\to \frac {c_1 e^{-\frac {\sqrt {a} x}{2}}}{\sqrt {x}}+\frac {c_2 e^{\frac {\sqrt {a} x}{2}}}{\sqrt {a} \sqrt {x}}\right \}\right \}\] Maple : cpu = 0.055 (sec), leaf count = 27


\[y \relax (x ) = \frac {c_{2} \cosh \left (\frac {\sqrt {a}\, x}{2}\right )+c_{1} \sinh \left (\frac {\sqrt {a}\, x}{2}\right )}{\sqrt {x}}\]