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 = 0.0450785 (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 = 0.063 (sec), leaf count = 35

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