Chapter 6.1, Problem 31E

To determine

(a)

To find:

$y^{\prime }$, $y^{″}$, and $y^{‴}$ for the set $y\left(x\right)=v\left(x\right)e^x$

To determine

(b)

To obtain:

The second-order differential equation by substituting $v^{\prime }=w$ in the $y^{‴}-2y^{″}-5y^{\prime }+6y=0,$

To determine

(c)

To solve:

The second-order differential equation $w^{″}+w^{\prime }-6w=0$ and find the linearly independent solution

To determine

(d)

To verify:

$e^x,y_1,y_2$ are linearly independent