91Ó°ÊÓ

Given interval is $-1<\mathrm{t}<1$. The given function can be Wronskian if the function is not equal to zero in the given interval.

Given function is$\mathrm{w}\left(\mathrm{t}\right)=6{\mathrm{e}}^{4\mathrm{t}}$

This function is always positive and cannot be zero in the interval $-1<\mathrm{t}<1$.Therefore, this function can be Wronskian.

Given function is$\mathrm{w}\left(\mathrm{t}\right)={\mathrm{t}}^3$

This function can be positive and negative and can be equal to zero in the interval $-1<\mathrm{t}<1$.Therefore, this function cannot be Wronskian.

Given function is$\mathrm{w}\left(\mathrm{t}\right)=(\mathrm{t}+1{)}^{-1}$

This function can be positive and negative and cannot be equal to zero in the interval $-1<\mathrm{t}<1$.

Therefore, this function can be Wronskian.

Given function is $\mathrm{w}\left(\mathrm{t}\right)≡0$

This function is always zero in the interval role="math" localid="1664187623401" $\mathbf{-}\mathbf{1}\mathbf{<}\mathbf{t}\mathbf{<}\mathbf{1}$.Therefore, this function cannot be Wronskian.

The given function can be Wronskian if the function is not equal to zero in the given interval.