2.1409   ODE No. 1409

\[ y''(x)=-b^2 x^{-2 a} y(x)-\frac {a y'(x)}{x} \] Mathematica : cpu = 0.0183538 (sec), leaf count = 43


\[\left \{\left \{y(x)\to c_1 \cos \left (\frac {b x^{1-a}}{a-1}\right )-c_2 \sin \left (\frac {b x^{1-a}}{a-1}\right )\right \}\right \}\] Maple : cpu = 0.016 (sec), leaf count = 39


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