Given that $y(t) = c_1 e^{4 t} + c_2 e^{-4 t}$ is a solution to the differential equation $y^{\,\prime\prime} - 16 y = 0$, where $c_1$ and $c_2$ are arbitrary constants, find a function $y(t)$ that satisfies the conditions

• $y^{\,\prime\prime} - 16 y = 0,$
  
  
• $y(0) = 6,$
  
  
• $\displaystyle \lim_{t \to +\infty} y(t) = 0.$

$y(t) =$ help (formulas)