$(1$ point$)$ Each graph below represents a solution to one of the following differential equations. Match the graph to the differential equation.

$($a$)x^{\text{'}\text{'}}+x=0$ matches graph $1vv$

$($b$)x^{\text{'}\text{'}}+4x=0$ matches graph

$($c$)x^{\text{'}\text{'}}+16x=0$ matches graph $4$

$($The $t-$scales on the four graphs are the same.$)$

$($d$)$ Find an equation for each of the graphs:

For graph $(1),x(t)=$

For graph $(2),x(t)=$

For graph $(3),x(t)=$

For graph $(4),x(t)=$