Multiple choice

A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system. $\begin{matrix} \ . \ \ y \ \end{matrix}$ (t) + 5y(t) = u(t) when y(0) = 1 and u(t) is a unit step function, y(t) is

  1. 0.2 + 0.8e-5t

  2. 0.2 - 0.2e-5t

  3. 0.8 + 0.2e-5t

  4. 0.8 - 0.8e-5t

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$y(t) = \frac{1}{5}u(t) + \frac{4}{5}e^{-5t} \\ \hspace{0.7cm} = 0.2 + 0.8 e^{-5t}$