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 = 0.111213 (sec), leaf count = 79

\[\left \{\left \{y(x)\to \frac {2 \left (c_2 e^{\frac {1}{2 x^2}} x \left (x^2-1\right )+8 c_1 \left (x^4+2 x^2-1\right )\right )-\sqrt {2 \pi } c_2 \left (x^4+2 x^2-1\right ) \text {erfi}\left (\frac {1}{\sqrt {2} x}\right )}{16 x}\right \}\right \}\]

Maple : cpu = 0.211 (sec), leaf count = 66

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