3.246   ODE No. 246

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

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

Mathematica: cpu = 0.031504 (sec), leaf count = 80 \[ \left \{\left \{y(x)\to \frac {1}{6} \left (-\frac {\sqrt {2} \sqrt {3 e^{4 c_1}-x^4}}{x}-4 x\right )\right \},\left \{y(x)\to \frac {1}{6} \left (\frac {\sqrt {2} \sqrt {3 e^{4 c_1}-x^4}}{x}-4 x\right )\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 63 \[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}\,x} \left ( -{\frac {2\,{x}^{2}{\it \_C1}}{3}}-{\frac {1}{6}\sqrt {-2\,{x}^{4}{{\it \_C1}} ^{2}+6}} \right ) },y \left ( x \right ) ={\frac {1}{{\it \_C1}\,x} \left ( -{\frac {2\,{x}^{2}{\it \_C1}}{3}}+{\frac {1}{6}\sqrt {-2\,{x} ^{4}{{\it \_C1}}^{2}+6}} \right ) } \right \} \]