3.28   ODE No. 28

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x \left ( y \left ( x \right ) \right ) ^{2}-{x}^{3}y \left ( x \right ) -2\,x=0} \]

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

Mathematica: cpu = 0.047006 (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 = 0.078 (sec), leaf count = 67 \[ \left \{ y \left ( x \right ) =2\,{\frac {{{\rm e}^{-1/4\,{x}^{4}}}{\it \_C1}}{\sqrt {\pi } \left ( {\it Erf} \left ( 1/2\,{x}^{2} \right ) {\it \_C1}+1 \right ) }}+{\frac {1}{\sqrt {\pi }} \left ( {\it Erf} \left ( { \frac {{x}^{2}}{2}} \right ) \sqrt {\pi }{\it \_C1}\,{x}^{2}+{x}^{2} \sqrt {\pi } \right ) \left ( {\it Erf} \left ( {\frac {{x}^{2}}{2}} \right ) {\it \_C1}+1 \right ) ^{-1}} \right \} \]

Sage: cpu = 0.096 (sec), leaf count = 0 \[ \left [\left [y\left (x\right ) = \frac {{\left ({\left (\sqrt {\pi } c \text {erf}\left (\frac {1}{2} \, x^{2}\right ) + \sqrt {\pi }\right )} x^{2} e^{\left (\frac {1}{4} \, x^{4}\right )} + 2 \, c\right )} e^{\left (-\frac {1}{4} \, x^{4}\right )}}{\sqrt {\pi } c \text {erf}\left (\frac {1}{2} \, x^{2}\right ) + \sqrt {\pi }}\right ], \text {\texttt {riccati}}\right ] \]