Based on a solution given as:
$x'' + 0.035x' + 0.00005x - 0.009 = 0$
Solve the characteristic equation. Based on your values of $r$, how large will $t$ have to be for the exponentials in the solution to have decayed to $2\%$ of their original value?
I solved the characteristic equation and got values of $r$ as $r = -0.0335$ and $r = -0.00149$. The solution then becomes:
$x(t) = c_1e^{-0.0335t}+c_2e^{-0.00149t}$
Now, how do I check what $t$ has to be for the exponentials to have decayed to $2\%$ of their value? Wouldn't I have to know $c_1$ and $c_2$?