Multiple choice

A solution for the differential equation $x(t) + 2x(t) = \delta(t)$with initial condition x (0 -) = 0 is

  1. e-2t u (t)

  2. e2t u (t)

  3. e-t u (t)

  4. et u (t)

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

$\text{We have} \hspace{0.5cm} x(t) + 2x(t) = \delta(t) \\ \text{Taking Laplace transform both sides} \\ sX(s) - x(0) + 2X(s) = 1 \\ or \hspace{2cm} sX(s) + 2X(s) = 1 \\ X(s) = \frac{1}{s+2} \\ \text{Now taking inverse laplace transform we have} \\ x(t) = e^{2t}u(t)$