Chapter 4.7, Problem 31E

(a)

To determine

Whether the function $w\left(t\right)=6e^{4t}$ can be Wronskian on $-1<t<1$ for a pair of solutions to some equation $y^{″}+p{y}^{\prime }+qy=0$, where $p\text{ and }q$ are constants.

(b)

To determine

Whether the function $w\left(t\right)=t^3$ can be Wronskian on $-1<t<1$ for a pair of solutions to some equation $y^{″}+p{y}^{\prime }+qy=0$, where $p\text{ and }q$ are constants.

(c)

To determine

Whether the function $w\left(t\right)={\left(t+1\right)}^{-1}$ can be Wronskian on $-1<t<1$ for a pair of solutions to some equation $y^{″}+p{y}^{\prime }+qy=0$, where $p\text{ and }q$ are constants.

(d)

To determine

Whether the function $w\left(t\right)\equiv 0$ can be Wronskian on $-1<t<1$ for a pair of solutions to some equation $y^{″}+p{y}^{\prime }+qy=0$, where $p\text{ and }q$ are constants.