$($a$)$ Show that any function of the form

$y=$Asinh$(mx)$ Bcosh$(mx)$

satisfies the differential equation $y^{\text{'}\text{'}}=m^{2}y.$

$($b$)$ Find $y=y(x)$ such that $y^{**}=25y,y(0)=-8,$ and $y^{\text{'}}(0)=15.$

$r(x)=$