3.182   ODE No. 182

\[ \boxed { x \left ( {x}^{3}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,x \left ( y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) +{x}^{2}=0} \]

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

Mathematica: cpu = 0.175022 (sec), leaf count = 96 \[ \left \{\left \{y(x)\to -\frac {\left (x^3-1\right ) \left (\frac {2 c_1 x^2}{\left (1-x^3\right )^{5/3}}+\frac {x}{\left (1-x^3\right )^{2/3}}+\frac {x^4}{\left (1-x^3\right )^{5/3}}\right )}{2 \left (\frac {c_1}{\left (1-x^3\right )^{2/3}}+\frac {x^2}{2 \left (1-x^3\right )^{2/3}}\right )}\right \}\right \} \]

Maple: cpu = 0.093 (sec), leaf count = 18 \[ \left \{ y \left ( x \right ) ={\frac {x \left ( x+{\it \_C1} \right ) }{{ \it \_C1}\,{x}^{2}+1}} \right \} \]