Chapter 3.4, Problem 20P

(a)

To determine

To show: The roots of the characteristic equation are $r_1=r_2=-a$, so that one solution of the equation is $e^{-at}$.

(b)

To determine

To show: The Wronskian of any two solution of the given equation is $W\left(t\right)=y_1\left(t\right){y^{\prime }}_2\left(t\right)-{y^{\prime }}_1\left(t\right)y_2\left(t\right)=c_1{e}^{-2at}$ where $c_1$ is a constant.

(c)

To determine

To show: The function $y_2\left(t\right)=t{e}^{-at}$  is a solution of the differential equation.