2.526   ODE No. 526

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

\[ -\left (x^2+x y(x)+y(x)^2\right ) y'(x)^2+\left (x^3 y(x)+x^2 y(x)^2+x y(x)^3\right ) y'(x)-x^3 y(x)^3+y'(x)^3=0 \] Mathematica : cpu = 0.0775332 (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 = 0.09 (sec), leaf count = 32

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