\[ y''(x)=-\frac {y(x) \left ((1-a) a x^2-b (b+x)\right )}{x^4} \] ✓ Mathematica : cpu = 0.162695 (sec), leaf count = 73
DSolve[Derivative[2][y][x] == -((((1 - a)*a*x^2 - b*(b + x))*y[x])/x^4),y[x],x]
\[\left \{\left \{y(x)\to c_1 \left (2 \left (a x+\frac {b}{2}\right ) I_a\left (\frac {b}{x}\right )+b I_{a+1}\left (\frac {b}{x}\right )\right )+c_2 \left (2 \left (a x+\frac {b}{2}\right ) K_a\left (\frac {b}{x}\right )-b K_{a+1}\left (\frac {b}{x}\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.086 (sec), leaf count = 58
dsolve(diff(diff(y(x),x),x) = -(x^2*a*(1-a)-b*(x+b))/x^4*y(x),y(x))
\[y \left (x \right ) = \BesselI \left (a +1, \frac {b}{x}\right ) c_{1} b -\BesselK \left (a +1, \frac {b}{x}\right ) c_{2} b +2 \left (c_{1} \BesselI \left (a , \frac {b}{x}\right )+c_{2} \BesselK \left (a , \frac {b}{x}\right )\right ) \left (a x +\frac {b}{2}\right )\]