Another DE problem.

Calculus Level 5

\(If\quad the\quad solution\quad to\quad the\quad DE\quad \\ \overset { \quad ... }{ y } +3\overset { \quad ..\quad }{ y } -4\overset { \quad .\quad }{ y } -12y=0,\quad y(0)=5;\quad \overset { \quad .\quad }{ y } (0)=2;\quad \\ \overset { \quad ..\quad }{ y } =30\quad can\quad be\quad written\quad as\quad a{ e }^{ bt }+csinh(dt)+ecosh(ft),\\ find\quad \begin{vmatrix} 1 & 1 & 1 \\ a & c & e \\ b & d & f \end{vmatrix}\)

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