What a differential?

$y$ is a thrice differentiable function that satisfy the differential equation $y''' + 3y'' - 4y' - 12 y = 0$ , where $y(0) = 5, y'(0) = 2, y''(0) = 30$ .

$y$ can be expressed as $A \cdot e^{Bt} + C \text{sinh}(Dt) + E \text{cosh}(Ft)$ , where $A,B,C,D,E,F$ are constants, and $e$ is Euler's number.

Evaluate the determinant of the matrix, $\begin{vmatrix}{1} && {1} && {1} \\ {A} && {C} && {E} \\ {B} && {D} && {F}\end{vmatrix}$ .