3.505   ODE No. 505

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

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

Mathematica: cpu = 0.013002 (sec), leaf count = 73 \[ \left \{\left \{y(x)\to -\sqrt {2 c_1+x^2}\right \},\left \{y(x)\to \sqrt {2 c_1+x^2}\right \},\left \{y(x)\to -\sqrt {c_1 x^4+x^2}\right \},\left \{y(x)\to \sqrt {c_1 x^4+x^2}\right \}\right \} \]

Maple: cpu = 0.032 (sec), leaf count = 52 \[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+{\it \_C1}},y \left ( x \right ) =\sqrt {{x}^{2}{\it \_C1}+1}x,y \left ( x \right ) =-\sqrt {{x} ^{2}+{\it \_C1}},y \left ( x \right ) =-\sqrt {{x}^{2}{\it \_C1}+1}x \right \} \]