#### 2.612   ODE No. 612

$y'(x)=\frac {1}{2} e^{\frac {x^2}{4}} \left (2 F\left (e^{-\frac {x^2}{4}} y(x)\right )+e^{-\frac {x^2}{4}} x y(x)\right )$ Mathematica : cpu = 0.331484 (sec), leaf count = 199

$\text {Solve}\left [\int _1^{y(x)}-\frac {e^{-\frac {x^2}{4}} \left (e^{\frac {x^2}{4}} F\left (e^{-\frac {x^2}{4}} K[2]\right ) \int _1^x\left (\frac {e^{-\frac {1}{4} K[1]^2} K[1]}{2 F\left (e^{-\frac {1}{4} K[1]^2} K[2]\right )}-\frac {e^{-\frac {1}{2} K[1]^2} K[1] K[2] F'\left (e^{-\frac {1}{4} K[1]^2} K[2]\right )}{2 F\left (e^{-\frac {1}{4} K[1]^2} K[2]\right )^2}\right )dK[1]+1\right )}{F\left (e^{-\frac {x^2}{4}} K[2]\right )}dK[2]+\int _1^x\left (\frac {e^{-\frac {1}{4} K[1]^2} K[1] y(x)}{2 F\left (e^{-\frac {1}{4} K[1]^2} y(x)\right )}+1\right )dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.101 (sec), leaf count = 27

$\left \{ y \left ( x \right ) ={{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \left ( {{\rm e}^{-{\frac {{x}^{2}}{4}}}} \right ) ^{-1}} \right \}$