3.402   ODE No. 402

\[ \boxed { 3\, \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+4\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) +{x}^{2}=0} \]

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

Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]

Maple: cpu = 0.577 (sec), leaf count = 121 \[ \left \{ y \left ( x \right ) =-{\frac {{x}^{2}}{3}},y \left ( x \right ) ={\frac {-2\,{\it \_C1}\,x \left ( -{\it \_C1}\,x+\sqrt {3} \right ) -5 \,{{\it \_C1}}^{2}{x}^{2}+3}{12\,{{\it \_C1}}^{2}}},y \left ( x \right ) ={\frac {2\,{\it \_C1}\,x \left ( {\it \_C1}\,x+\sqrt {3} \right ) -5\,{{\it \_C1}}^{2}{x}^{2}+3}{12\,{{\it \_C1}}^{2}}},y \left ( x \right ) =-{\frac {5\,{x}^{2}}{12}}-{\frac {x \left ( -x- \sqrt {3}{\it \_C1} \right ) }{6}}+{\frac {{{\it \_C1}}^{2}}{4}},y \left ( x \right ) =-{\frac {5\,{x}^{2}}{12}}-{\frac {x \left ( -x+ \sqrt {3}{\it \_C1} \right ) }{6}}+{\frac {{{\it \_C1}}^{2}}{4}} \right \} \]