2.296   ODE No. 296

\[ x^4+x \left (x^2 y(x)+x^2+y(x)^2\right ) y'(x)-2 x^2 y(x)^2-2 y(x)^3=0 \] Mathematica : cpu = 0.447394 (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 = 0.592 (sec), leaf count = 135


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