Select the correct choice below and fill $in$ any answer boxes $to$ complete your choice.

$A.$ A solution $is$ guaranteed only $at$ the point $t_0=$

because the functions $p(t)=$

$.q(t)=,$ and $g(t)=$

are simultaneously defined $at$ that point.

$B.$ A solution $is$ guaranteed $on$ the interval $t_0=p(t)=,q(t)=,g(t)=t_0=p(t)=,q(t)=ag(t)=$ because $it$ contains the point $t_0=$ and the functions $p(t)=,q(t)=$a and $g(t)=$

are simultaneously continuous $on$ the interval. because $it$ contains the point $t_0=$

and the functions $p(t)=,q(t)=,$ and $g(t)=$

are equal $on$ the interval.

$C.$ A solution $is$ guaranteed $on$ the interval because $it$ contains the point $t_0=$ and the functions $p(t)=,q(t)=$a and $g(t)=$

are simultaneously continuous $on$ the interval.