\[ y''(x)=-\frac {2 (a+x) y'(x)}{x^2}-\frac {b y(x)}{x^4} \] ✓ Mathematica : cpu = 0.0098702 (sec), leaf count = 89
DSolve[Derivative[2][y][x] == -((b*y[x])/x^4) - (2*(a + x)*Derivative[1][y][x])/x^2,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{-\frac {\sqrt {b} \left (-\frac {\sqrt {a^2-b}}{\sqrt {b}}-\frac {a}{\sqrt {b}}\right )}{x}}+c_2 e^{-\frac {\sqrt {b} \left (\frac {\sqrt {a^2-b}}{\sqrt {b}}-\frac {a}{\sqrt {b}}\right )}{x}}\right \}\right \}\] ✓ Maple : cpu = 0.042 (sec), leaf count = 43
dsolve(diff(diff(y(x),x),x) = -2/x^2*(x+a)*diff(y(x),x)-b/x^4*y(x),y(x))
\[y \left (x \right ) = c_{1} {\mathrm e}^{\frac {-\sqrt {a^{2}-b}+a}{x}}+c_{2} {\mathrm e}^{\frac {\sqrt {a^{2}-b}+a}{x}}\]