2.28   ODE No. 28

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

\[ x^3 (-y(x))+y'(x)+x y(x)^2-2 x=0 \] Mathematica : cpu = 0.0482776 (sec), leaf count = 96

\[\left \{\left \{y(x)\to \frac {c_1 e^{\frac {x^4}{4}} x^3+\frac {1}{2} \sqrt {\pi } e^{\frac {x^4}{4}} x^3 \text {erf}\left (\frac {x^2}{2}\right )+x}{x \left (c_1 e^{\frac {x^4}{4}}+\frac {1}{2} \sqrt {\pi } e^{\frac {x^4}{4}} \text {erf}\left (\frac {x^2}{2}\right )\right )}\right \}\right \}\]

Maple : cpu = 0.086 (sec), leaf count = 67

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