4.354   ODE No. 1354

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) ={\frac { \left ( 2\,{x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{3}}}-2\,{\frac {y \left ( x \right ) }{{x}^{4}}}=0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.071009 (sec), leaf count = 108 \[ \left \{\left \{y(x)\to \frac {c_2 \left (-5 \sqrt {2 \pi } x^2 \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )+\sqrt {2 \pi } \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )-2 e^{\frac {1}{2 x^2}} x+4 e^{\frac {1}{2 x^2}} x^5+8 e^{\frac {1}{2 x^2}} x^3\right )}{12 x^2}+c_1 \left (1-\frac {1}{5 x^2}\right )\right \}\right \} \]

Maple: cpu = 0.156 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( 5\,{x}^{2}-1 \right ) }{{x}^{2}}}+{\it \_C2}\, {\mbox {$_1$F$_1$}(-{\frac {5}{2}};\,-{\frac {1}{2}};\,{\frac {1}{2\,{x}^{2}}})} {x}^{3} \right \} \]