\[ y''(x)=-b^2 x^{-2 a} y(x)-\frac {a y'(x)}{x} \] ✓ Mathematica : cpu = 0.0183538 (sec), leaf count = 43
DSolve[Derivative[2][y][x] == -((b^2*y[x])/x^(2*a)) - (a*Derivative[1][y][x])/x,y[x],x]
\[\left \{\left \{y(x)\to c_1 \cos \left (\frac {b x^{1-a}}{a-1}\right )-c_2 \sin \left (\frac {b x^{1-a}}{a-1}\right )\right \}\right \}\] ✓ Maple : cpu = 0.016 (sec), leaf count = 39
dsolve(diff(diff(y(x),x),x) = -a*x^(2*a-1)/(x^(2*a))*diff(y(x),x)-b^2/(x^(2*a))*y(x),y(x))
\[y \left (x \right ) = c_{1} \sin \left (\frac {x^{1-a} b}{a -1}\right )+c_{2} \cos \left (\frac {x^{1-a} b}{a -1}\right )\]