2.296   ODE No. 296

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

\[ x \left (x^2 y(x)+x^2+y(x)^2\right ) y'(x)-2 x^2 y(x)^2+x^4-2 y(x)^3=0 \] Mathematica : cpu = 0.496439 (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 = 0.563 (sec), leaf count = 135

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