\[ y''(x)=-\frac {y(x)}{x^4}-\frac {\left (x^2+1\right ) y'(x)}{x^3} \] ✓ Mathematica : cpu = 0.0938821 (sec), leaf count = 76
DSolve[Derivative[2][y][x] == -(y[x]/x^4) - ((1 + x^2)*Derivative[1][y][x])/x^3,y[x],x]
\[\left \{\left \{y(x)\to c_2 G_{1,2}^{2,0}\left (-\frac {1}{2 x^2}|\begin {array}{c} \frac {3}{2} \\ 0,0 \\\end {array}\right )+c_1 e^{\frac {1}{4 x^2}} \left (\left (1-\frac {1}{2 x^2}\right ) I_0\left (\frac {1}{4 x^2}\right )+\frac {I_1\left (\frac {1}{4 x^2}\right )}{2 x^2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.067 (sec), leaf count = 85
dsolve(diff(diff(y(x),x),x) = -(x^2+1)/x^3*diff(y(x),x)-1/x^4*y(x),y(x))
\[y \left (x \right ) = \frac {c_{1} {\mathrm e}^{\frac {1}{4 x^{2}}} \left (2 \BesselI \left (0, \frac {1}{4 x^{2}}\right ) x^{2}-\BesselI \left (0, \frac {1}{4 x^{2}}\right )+\BesselI \left (1, \frac {1}{4 x^{2}}\right )\right )}{x^{2}}+\frac {c_{2} {\mathrm e}^{\frac {1}{4 x^{2}}} \left (2 \BesselK \left (0, -\frac {1}{4 x^{2}}\right ) x^{2}-\BesselK \left (0, -\frac {1}{4 x^{2}}\right )+\BesselK \left (1, -\frac {1}{4 x^{2}}\right )\right )}{x^{2}}\]