ODE No. 526

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

\[ -x^3 y(x)^3-\left (x^2+x y(x)+y(x)^2\right ) y'(x)^2+\left (x^3 y(x)+x^2 y(x)^2+x y(x)^3\right ) y'(x)+y'(x)^3=0 \] Mathematica : cpu = 1.15531 (sec), leaf count = 45

\[\left \{\left \{y(x)\to \frac {1}{-c_1-x}\right \},\left \{y(x)\to c_1 e^{\frac {x^2}{2}}\right \},\left \{y(x)\to c_1+\frac {x^3}{3}\right \}\right \}\] Maple : cpu = 0.02 (sec), leaf count = 32

\[ \left \{ y \left ( x \right ) = \left ( -x+{\it \_C1} \right ) ^{-1},y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}},y \left ( x \right ) ={\frac {{x}^{3}}{3}}+{\it \_C1} \right \} \]