Consider the differential equation for the function y$($t$)$y$($t$),$

y$+5$y$+4$y$=0$y$+5$y$+4$y$=0$

Where does the characteristic equation come from?

$$Choose One.$$From substituing y$($t$)=$ ln$($rt$)$ in the differential equation.$$From substituing y$($t$)=$ e$^($rt$)$ in the differential equation.$$From substituing y$($t$)=$ sin$($rt$)$ in the differential equation.$$From substituing y$($t$)=$ t$^$r in the differential equation.$$From substituing y$($t$)=$ cos$($rt$)$ in the differential equation.$$From substituing y$($t$)=$ r in the differential equation.$$

What is the characteristic equation of the differential equation above?

A$.$ r$2=0$r$2=0$

B$.$ r$2+5$r$+4=0$r$2+5$r$+4=0$

C$.$ r$25$r$4=0$r$25$r$4=0$

D$.$ r$2+5$rt$+4$t$2=0$r$2+5$rt$+4$t$2=0$

E$.($r$+5)2+4=0($r$+5)2+4=0$

F$.$ r$25$r$+4=0$r$25$r$+4=0$