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 = 0.57085 (sec), leaf count = 88

\[\left \{\left \{y(x)\to -e^{-c_1} \left (\sqrt {x^2 \left (-e^{c_1} x^2+e^{2 c_1}+x^2\right )}+x^2\right )\right \},\left \{y(x)\to e^{-c_1} \left (\sqrt {x^2 \left (-e^{c_1} x^2+e^{2 c_1}+x^2\right )}-x^2\right )\right \}\right \}\]

Maple : cpu = 0.779 (sec), leaf count = 135

\[ \left \{ y \left ( x \right ) =-{x \left ( -{x}^{3}+{\it \_C1}\,x+{x}^{2}+\sqrt {-{\it \_C1}\,{x}^{4}+{{\it \_C1}}^{2}{x}^{2}+{x}^{4}} \right ) \left ( {\it \_C1}\,x-{x}^{2}+\sqrt {-{\it \_C1}\,{x}^{4}+{{\it \_C1}}^{2}{x}^{2}+{x}^{4}} \right ) ^{-1}},y \left ( x \right ) =-{x \left ( {x}^{3}-{\it \_C1}\,x-{x}^{2}+\sqrt {-{\it \_C1}\,{x}^{4}+{{\it \_C1}}^{2}{x}^{2}+{x}^{4}} \right ) \left ( -{\it \_C1}\,x+{x}^{2}+\sqrt {-{\it \_C1}\,{x}^{4}+{{\it \_C1}}^{2}{x}^{2}+{x}^{4}} \right ) ^{-1}} \right \} \]