This question is concerned with the differential equation

$4\frac{d^{2}x}{d{t}^2}+48\frac{dx}{dt}+288x=0$

$($a$)$ Find the general solution of this differential equation.

Leave out the $"x="$

$(5$ marks$)$

This question accepts numbers or formulas.

$($b$)$ Find the particular solution for the differential equation if $x=0$ and $\frac{dx}{dt}=270$ when $t=0.$

Leave out the $"x="$

Leave any numbers, which are not whole numbers, as FRACTIONS

$(5$ marks$)$

This question accepts numbers or formulas.

$($c$)$ Find the value of x at $t=0\mathrm{.}2618$

$.$ Insert only the number and give it to AT LEAST FOUR DECIMAL PLACES. $(2$ marks$)$