2.864   ODE No. 864

\[ y'(x)=\frac {e^{\frac {x^2}{4}} y(x) \left (2 e^{-\frac {3 x^2}{4}} y(x)^2+e^{-\frac {x^2}{2}} x y(x)+e^{-\frac {x^2}{4}} x\right )}{2 e^{-\frac {x^2}{4}} y(x)+2} \] Mathematica : cpu = 0.32708 (sec), leaf count = 137


\[\left \{\left \{y(x)\to \frac {2 e^{\frac {x^2}{2}}}{-2 e^{\frac {x^2}{4}}+\sqrt {2} \sqrt {2 e^{\frac {x^2}{2}}+2 e^{\frac {x^2}{2}} (-2 x+c_1)}}\right \},\left \{y(x)\to -\frac {2 e^{\frac {x^2}{2}}}{2 e^{\frac {x^2}{4}}+\sqrt {2} \sqrt {2 e^{\frac {x^2}{2}}+2 e^{\frac {x^2}{2}} (-2 x+c_1)}}\right \}\right \}\] Maple : cpu = 0.085 (sec), leaf count = 162


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