Chapter 9.4, Problem 37E

To determine

(a)

To show:

That $\left\{e^t,e^{2t},e^{3t}\right\}$ is a fundamental solution set

To determine

(b)

To find:

The Wronskian of $\left\{e^t,e^{2t},e^{3t}\right\}$.

To determine

(c)

To show:

The equation $y^{‴}\left(t\right)-6y^{″}\left(t\right)+11y^{\prime }\left(t\right)-6y\left(t\right)=0$ is equivalent to the first-order system $x^{\prime }=Ax$.

To determine

(d)

To verify:

The solution set.

To determine

(d)

To find:

The Wronskian of $S$.