2.1353   ODE No. 1353

\[ y''(x)=\frac {\left (2 x^2-1\right ) y'(x)}{x^3}-\frac {y(x)}{x^4} \] Mathematica : cpu = 0.731211 (sec), leaf count = 119


\[\left \{\left \{y(x)\to c_1 \left (x^3+2 x-\frac {1}{x}\right )-\frac {c_2 \left (\sqrt {2 \pi } x^4 \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )+2 \sqrt {2 \pi } x^2 \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )-\sqrt {2 \pi } \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )+2 e^{\frac {1}{2 x^2}} x-2 e^{\frac {1}{2 x^2}} x^3\right )}{16 x}\right \}\right \}\] Maple : cpu = 0.217 (sec), leaf count = 66


\[y \relax (x ) = \frac {c_{1} \sqrt {2}\, \sqrt {\pi }\, \left (x^{4}+2 x^{2}-1\right ) \erfi \left (\frac {\sqrt {2}}{2 x}\right )+\left (-2 x^{3} c_{1}+2 c_{1} x \right ) {\mathrm e}^{\frac {1}{2 x^{2}}}+c_{2} \left (x^{4}+2 x^{2}-1\right )}{x}\]