2.296   ODE No. 296

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

\[ x^4+x \left (x^2 y(x)+x^2+y(x)^2\right ) y'(x)-2 x^2 y(x)^2-2 y(x)^3=0 \] Mathematica : cpu = 0.536607 (sec), leaf count = 102

\[\left \{\left \{y(x)\to -e^{-c_1} x^2-e^{-c_1} \sqrt {x^4-e^{c_1} x^4+e^{2 c_1} x^2}\right \},\left \{y(x)\to e^{-c_1} \sqrt {x^4-e^{c_1} x^4+e^{2 c_1} x^2}-e^{-c_1} x^2\right \}\right \}\] Maple : cpu = 0.599 (sec), leaf count = 135

\[\left \{y \left (x \right ) = -\frac {\left (-x^{3}+c_{1} x +x^{2}+\sqrt {-c_{1} x^{4}+x^{4}+c_{1}^{2} x^{2}}\right ) x}{c_{1} x -x^{2}+\sqrt {-c_{1} x^{4}+x^{4}+c_{1}^{2} x^{2}}}, y \left (x \right ) = -\frac {\left (x^{3}-c_{1} x -x^{2}+\sqrt {-c_{1} x^{4}+x^{4}+c_{1}^{2} x^{2}}\right ) x}{-c_{1} x +x^{2}+\sqrt {-c_{1} x^{4}+x^{4}+c_{1}^{2} x^{2}}}\right \}\]