3.296   ODE No. 296

\[ \boxed { x \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}y \left ( x \right ) +{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\, \left ( y \left ( x \right ) \right ) ^{3}-2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{4}=0} \]

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

Mathematica: cpu = 0.571072 (sec), leaf count = 102 \[ \left \{\left \{y(x)\to -e^{-c_1} x^2-e^{-c_1} \sqrt {-e^{c_1} x^4+e^{2 c_1} x^2+x^4}\right \},\left \{y(x)\to e^{-c_1} \sqrt {-e^{c_1} x^4+e^{2 c_1} x^2+x^4}-e^{-c_1} x^2\right \}\right \} \]

Maple: cpu = 0.562 (sec), leaf count = 165 \[ \left \{ y \left ( x \right ) =-{{x}^{3} \left ( x-2 \right ) \left ( { \frac {1}{ \left ( x-2 \right ) {x}^{2}} \left ( {\it \_C1}\,x-{x}^{2}- \sqrt {-{\it \_C1}\,{x}^{4}+{{\it \_C1}}^{2}{x}^{2}+{x}^{4}} \right ) } -1 \right ) \left ( {\it \_C1}\,x-{x}^{2}-\sqrt {-{\it \_C1}\,{x}^{4}+{ {\it \_C1}}^{2}{x}^{2}+{x}^{4}} \right ) ^{-1}},y \left ( x \right ) =-{{ x}^{3} \left ( x-2 \right ) \left ( {\frac {1}{ \left ( x-2 \right ) {x}^{ 2}} \left ( {\it \_C1}\,x-{x}^{2}+\sqrt {-{\it \_C1}\,{x}^{4}+{{\it \_C1}}^{2}{x}^{2}+{x}^{4}} \right ) }-1 \right ) \left ( {\it \_C1}\,x-{ x}^{2}+\sqrt {-{\it \_C1}\,{x}^{4}+{{\it \_C1}}^{2}{x}^{2}+{x}^{4}} \right ) ^{-1}} \right \} \]