2.526   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 = 0.0770687 (sec), leaf count = 45

\[\left \{\left \{y(x)\to \frac {1}{-x-c_1}\right \},\left \{y(x)\to c_1 e^{\frac {x^2}{2}}\right \},\left \{y(x)\to \frac {x^3}{3}+c_1\right \}\right \}\] Maple : cpu = 0.016 (sec), leaf count = 32

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