\[ y''(x)=\frac {\left (2 x^2-1\right ) y'(x)}{x^3}-\frac {y(x)}{x^4} \] ✓ Mathematica : cpu = 0.554192 (sec), leaf count = 119
DSolve[Derivative[2][y][x] == -(y[x]/x^4) + ((-1 + 2*x^2)*Derivative[1][y][x])/x^3,y[x],x]
\[\left \{\left \{y(x)\to c_1 \left (x^3+2 x-\frac {1}{x}\right )-\frac {c_2 \left (\sqrt {2 \pi } x^4 \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )+2 \sqrt {2 \pi } x^2 \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )-\sqrt {2 \pi } \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )+2 e^{\frac {1}{2 x^2}} x-2 e^{\frac {1}{2 x^2}} x^3\right )}{16 x}\right \}\right \}\] ✓ Maple : cpu = 0.291 (sec), leaf count = 65
dsolve(diff(diff(y(x),x),x) = 1/x^3*(2*x^2-1)*diff(y(x),x)-1/x^4*y(x),y(x))
\[y \left (x \right ) = \frac {-c_{1} \sqrt {2}\, \sqrt {\pi }\, \left (x^{4}+2 x^{2}-1\right ) \operatorname {erfi}\left (\frac {\sqrt {2}}{2 x}\right )+2 c_{1} \left (x^{3}-x \right ) {\mathrm e}^{\frac {1}{2 x^{2}}}+c_{2} \left (x^{4}+2 x^{2}-1\right )}{x}\]