4.353   ODE No. 1353

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

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

Mathematica: cpu = 0.107514 (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 = 0.141 (sec), leaf count = 68 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{x} \left ( \sqrt {2} \sqrt {\pi } \left ( {x}^{4}+2\,{x}^{2}-1 \right ) {\it erfi} \left ( { \frac {\sqrt {2}}{2\,x}} \right ) + \left ( -2\,{x}^{3}+2\,x \right ) { {\rm e}^{{\frac {1}{2\,{x}^{2}}}}} \right ) }+{\frac {{\it \_C2}\, \left ( {x}^{4}+2\,{x}^{2}-1 \right ) }{x}} \right \} \]