\[ y''(x)=-b^2 x^{-2 a} y(x)-\frac {a y'(x)}{x} \] ✓ Mathematica : cpu = 0.025523 (sec), leaf count = 44
\[\left \{\left \{y(x)\to c_2 \sin \left (\frac {b x^{1-a}}{1-a}\right )+c_1 \cos \left (\frac {b x^{1-a}}{a-1}\right )\right \}\right \}\]
✓ Maple : cpu = 0.016 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( {\frac {{x}^{1-a}b}{a-1}} \right ) +{\it \_C2}\,\cos \left ( {\frac {{x}^{1-a}b}{a-1}} \right ) \right \} \]