Which of the following is the general solution of d²y/dx² – 2(dy/dx) + y = 0

The correct option is y = (Ax + B)e^x.

To find the general solution of the given second-order linear homogeneous differential equation with constant coefficients:
$$\frac{d^{2}y}{d{x}^2}-2\frac{dy}{dx}+y=0$$
we first write down its characteristic (or auxiliary) equation.

By substituting $y=e^{rx}$, we obtain the auxiliary quadratic equation:
$$r^2-2r+1=0$$

We can solve this quadratic equation by factoring it:
$${(r-1)}^2=0$$
This gives a repeated real root:
$$r=1$$

When the characteristic equation has a repeated real root $r$ of multiplicity 2, the general solution of the differential equation is of the form:
$$y=(Ax+B)e^{rx}$$
where $A$ and $B$ are arbitrary constants.

Substituting $r=1$ into the general form, we get:
$$y=(Ax+B)e^x$$
This matches the correct option exactly.