2.1208   ODE No. 1208

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

\[ x^3 y'(x)+x^2 y''(x)+\left (x^2-2\right ) y(x)=0 \] Mathematica : cpu = 0.0470233 (sec), leaf count = 59

\[\left \{\left \{y(x)\to \frac {c_2 e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } e^{\frac {x^2}{2}} \text {erf}\left (\frac {x}{\sqrt {2}}\right )-2 x\right )}{2 x}+\frac {c_1}{x}\right \}\right \}\] Maple : cpu = 0.056 (sec), leaf count = 35

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