3.439   ODE No. 439

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

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

Mathematica: cpu = 0.034504 (sec), leaf count = 49 \[ \left \{\left \{y(x)\to c_1 x^{\frac {1}{2} \left (-3-i \sqrt {3}\right )}\right \},\left \{y(x)\to c_1 x^{\frac {1}{2} i \left (\sqrt {3}+3 i\right )}\right \}\right \} \]

Maple: cpu = 0.546 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={{\it \_C1}\,{x}^{-{\frac {i}{2}}\sqrt {3 }}{x}^{-{\frac {3}{2}}}},y \left ( x \right ) ={{\it \_C1}\,{x}^{{\frac {i}{2}}\sqrt {3}}{x}^{-{\frac {3}{2}}}} \right \} \]