ODE No. 505

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

\[ -x^3+x y(x)^2 y'(x)^2-2 y(x)^3 y'(x)+2 x y(x)^2=0 \] Mathematica : cpu = 0.031146 (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 = 0.039 (sec), leaf count = 52

\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+{\it \_C1}},y \left ( x \right ) =\sqrt {{\it \_C1}\,{x}^{2}+1}x,y \left ( x \right ) =-\sqrt {{x}^{2}+{\it \_C1}},y \left ( x \right ) =-\sqrt {{\it \_C1}\,{x}^{2}+1}x \right \} \]