Question $1$

What $is$ the general solution $to$ the following equation?

$3x^{\text{'}\text{'}}+4x^{\text{'}}+5x=0$

Choose one answer only:

$(a)x(t)=c_1{e}^{r_{1}t}+c_2{e}^{r_{2}t}$

$(b)x(t)=c_1{e}^{rt}+c_{2}t{e}^{rt}$

$(c)x(t)=e^t(c_{1}cost+c_{2}sint)$

$(a)$

$(b)$

$(c)$