Using the Wronskian, verify that the given functions form a fundamental solution set for the given differential equation and find a general solution.

$y^{(4)}-y=0$;$\{e^x,e^{-x},cosx,sinx\}$

What should be done to verify that the given set of functions forms a fundamental solution set to the given differential equation? Select the correct choice below and fill in the answer box to complete your choice.

$($Simplify your answer.$)$

A$.$ Verify that each function satisfies the given differential equation and then verify that $W[e^x,e^{-x},cosx,sinx]=$

$$ B$.$ Verify that each function satisfies the given differential equation and then verify that $w[e^x,e^{-x},cosx,sinx]0.$

Find $\frac{d^4}{d{x}^4}{e}^x$

$\frac{d^4}{d{x}^4}{e}^x=$

Substituting $y=e^x$ and $y^{(4)}=\frac{d^4}{e^x}$ into the differential equation yields a true statement. Now find $\frac{d^4}{d^4}{e}^{-x}$