Chapter 4.CR, Problem 89CR

To determine

(a)

To find:

Whether the function $e^{-2x}$ is a solution of the linear differential equation $y^{\prime }+2y=0$.

To determine

(b)

To find:

Whether the function $x{e}^{-2x}$ is a solution of the linear differential equation $y^{\prime }+2y=0$.

To determine

(c)

To find:

Whether the function $x^2{e}^{-x}$ is a solution of the linear differential equation $y^{\prime }+2y=0$.

To determine

(d)

To find:

Whether the function $2x{e}^{-2x}$ is a solution of the linear differential equation $y^{\prime }+2y=0$.