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 = 0.280505 (sec), leaf count = 137

$\left \{\left \{y(x)\to \frac {2 e^{\frac {x^2}{2}}}{\sqrt {2} \sqrt {2 e^{\frac {x^2}{2}} (c_1-2 x)+2 e^{\frac {x^2}{2}}}-2 e^{\frac {x^2}{4}}}\right \},\left \{y(x)\to -\frac {2 e^{\frac {x^2}{2}}}{\sqrt {2} \sqrt {2 e^{\frac {x^2}{2}} (c_1-2 x)+2 e^{\frac {x^2}{2}}}+2 e^{\frac {x^2}{4}}}\right \}\right \}$ Maple : cpu = 0.06 (sec), leaf count = 162

$\left \{ y \left ( x \right ) ={1 \left ( {{\rm e}^{{\frac {{x}^{2}}{2}}}} \left ( \sqrt {{\it \_C1}-2\,x}-1 \right ) {{\rm e}^{-{\frac {{x}^{2}}{4}}}}-{{\rm e}^{{\frac {{x}^{2}}{4}}}}\sqrt {{\it \_C1}-2\,x} \right ) \left ( {{\rm e}^{-{\frac {{x}^{2}}{4}}}} \right ) ^{-1} \left ( {{\rm e}^{{\frac {{x}^{2}}{4}}}}\sqrt {{\it \_C1}-2\,x}+{{\rm e}^{-{\frac {{x}^{2}}{4}}}}{{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) ^{-1}},y \left ( x \right ) ={1 \left ( {{\rm e}^{{\frac {{x}^{2}}{2}}}} \left ( \sqrt {{\it \_C1}-2\,x}+1 \right ) {{\rm e}^{-{\frac {{x}^{2}}{4}}}}-{{\rm e}^{{\frac {{x}^{2}}{4}}}}\sqrt {{\it \_C1}-2\,x} \right ) \left ( {{\rm e}^{-{\frac {{x}^{2}}{4}}}} \right ) ^{-1} \left ( {{\rm e}^{{\frac {{x}^{2}}{4}}}}\sqrt {{\it \_C1}-2\,x}-{{\rm e}^{-{\frac {{x}^{2}}{4}}}}{{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) ^{-1}} \right \}$