The general form of the complementary function of a differential equation is given by $y(t) = (At + B)e^{-2t}$, where $A$ and $B$ are real constants determined by the initial condition. The corresponding differential equation is ____.

Consider the following partial differential equation (PDE)

$$a{{{\partial ^2}f(x,y)} \over {\partial {x^2}}} + b{{{\partial ^2}f(x,y)} \over {\partial {y^2}}} = f(x,y)$$,

where a and b are distinct positive real numbers. Select the combination(s) of values of the real parameters $$\xi $$ and $$\eta $$ such that $$f(x,y) = {e^{\xi x + \eta y}}$$ is a solution of the given PDE.

The general solution of $\frac{d^2 y}{d x^2}-6 \frac{d y}{d x}+9 y=0$ is