2.1353   ODE No. 1353

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

\[ y''(x)=\frac {\left (2 x^2-1\right ) y'(x)}{x^3}-\frac {y(x)}{x^4} \] Mathematica : cpu = 0.10906 (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 = 0.416 (sec), leaf count = 68

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{x} \left ( \sqrt {2}\sqrt {\pi } \left ( {x}^{4}+2\,{x}^{2}-1 \right ) {\it erfi} \left ( {\frac {\sqrt {2}}{2\,x}} \right ) + \left ( -2\,{x}^{3}+2\,x \right ) {{\rm e}^{{\frac {1}{2\,{x}^{2}}}}} \right ) }+{\frac {{\it \_C2}\, \left ( {x}^{4}+2\,{x}^{2}-1 \right ) }{x}} \right \} \]