#### 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 = 0.28418 (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 = 0.145 (sec), leaf count = 162

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