DSolve[Derivative[1][y][x] == (E^(x^2/4)*y[x]*(x/E^(x^2/4) + (x*y[x])/E^(x^2/2) + (2*y[x]^2)/E^((3*x^2)/4)))/(2 + (2*y[x])/E^(x^2/4)),y[x],x]