2.1170   ODE No. 1170

\[ y(x) \left (a x^2+b\right )+x^2 y''(x)+2 x y'(x)=0 \] Mathematica : cpu = 0.0155376 (sec), leaf count = 58


\[\left \{\left \{y(x)\to c_1 j_{\frac {1}{2} \left (\sqrt {1-4 b}-1\right )}\left (\sqrt {a} x\right )+c_2 y_{\frac {1}{2} \left (\sqrt {1-4 b}-1\right )}\left (\sqrt {a} x\right )\right \}\right \}\] Maple : cpu = 0.043 (sec), leaf count = 43


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