2.281   ODE No. 281

\[ \left (-x^2+2 x y(x)+y(x)^2\right ) y'(x)+x^2+2 x y(x)-y(x)^2=0 \] Mathematica : cpu = 0.195536 (sec), leaf count = 75


\[\left \{\left \{y(x)\to \frac {1}{2} \left (e^{c_1}-\sqrt {-4 x^2+4 e^{c_1} x+e^{2 c_1}}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {-4 x^2+4 e^{c_1} x+e^{2 c_1}}+e^{c_1}\right )\right \}\right \}\] Maple : cpu = 0.048 (sec), leaf count = 55


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