2.1376   ODE No. 1376

\[ y''(x)=-\frac {b y(x)}{x^2 \left (a+x^2\right )}-\frac {\left (a+2 x^2\right ) y'(x)}{x \left (a+x^2\right )} \] Mathematica : cpu = 0.0294589 (sec), leaf count = 69


\[\left \{\left \{y(x)\to c_1 \cos \left (\frac {\sqrt {b} \tanh ^{-1}\left (\frac {\sqrt {a+x^2}}{\sqrt {a}}\right )}{\sqrt {a}}\right )-c_2 \sin \left (\frac {\sqrt {b} \tanh ^{-1}\left (\frac {\sqrt {a+x^2}}{\sqrt {a}}\right )}{\sqrt {a}}\right )\right \}\right \}\] Maple : cpu = 0.05 (sec), leaf count = 73


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