\[ y''(x)=-\frac {a y(x)}{x^4} \] ✓ Mathematica : cpu = 0.081132 (sec), leaf count = 52
DSolve[Derivative[2][y][x] == -((a*y[x])/x^4),y[x],x]
\[\left \{\left \{y(x)\to c_1 x e^{\frac {i \sqrt {a}}{x}}-\frac {i c_2 x e^{-\frac {i \sqrt {a}}{x}}}{2 \sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.027 (sec), leaf count = 31
dsolve(diff(diff(y(x),x),x) = -a/x^4*y(x),y(x))
\[y \left (x \right ) = x \left (\cosh \left (\frac {\sqrt {-a}}{x}\right ) c_{2}+\sinh \left (\frac {\sqrt {-a}}{x}\right ) c_{1}\right )\]