3.29   ODE No. 29

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

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

Mathematica: cpu = 0.022003 (sec), leaf count = 39 \[ \left \{\left \{y(x)\to -\frac {3 e^{3 c_1+\frac {3 x^2}{2}}}{e^{3 c_1+\frac {3 x^2}{2}}-1}\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 19 \[ \left \{ y \left ( x \right ) =3\, \left ( -1+3\,{{\rm e}^{-3/2\,{x}^{2}} }{\it \_C1} \right ) ^{-1} \right \} \]

Sage: cpu = 0.056 (sec), leaf count = 0 \[ \left [-\frac {1}{3} \, \log \left (y\left (x\right ) + 3\right ) + \frac {1}{3} \, \log \left (y\left (x\right )\right ) = \frac {1}{2} \, x^{2} + c, \text {\texttt {separable}}\right ] \]