\[ y''(x)=\frac {\left (2 x^2-1\right ) y'(x)}{x^3}-\frac {2 y(x)}{x^4} \] ✓ Mathematica : cpu = 0.212802 (sec), leaf count = 108
DSolve[Derivative[2][y][x] == (-2*y[x])/x^4 + ((-1 + 2*x^2)*Derivative[1][y][x])/x^3,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_2 \left (-5 \sqrt {2 \pi } x^2 \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )+\sqrt {2 \pi } \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )-2 e^{\frac {1}{2 x^2}} x+4 e^{\frac {1}{2 x^2}} x^5+8 e^{\frac {1}{2 x^2}} x^3\right )}{12 x^2}+c_1 \left (1-\frac {1}{5 x^2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.271 (sec), leaf count = 33
dsolve(diff(diff(y(x),x),x) = 1/x^3*(2*x^2-1)*diff(y(x),x)-2/x^4*y(x),y(x))
\[y \left (x \right ) = \frac {c_{2} \hypergeom \left (\left [-\frac {5}{2}\right ], \left [-\frac {1}{2}\right ], \frac {1}{2 x^{2}}\right ) x^{5}+5 c_{1} x^{2}-c_{1}}{x^{2}}\]