Question

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.

y(t) + 5y(t) = u(t)

When y(0) = 1 and u(t) is a unit step function, y(t) is

(A) 0.2 + 0.8e-5t

(B) 0.2 - 0.2e-5t

(C) 0.8 + 0.2e-5t

(D) 0.8 - 0.8e-5t

Answer 1

Given y(t) + 5y(t) = u(t) and y(0) = 1; u(t) is a unit step function.

Apply Laplace transform to the given differential equation.

Sy() - y(0) + 5y() = 1/*

y()[ + 5] = 1/ + y(0) [L[dy/dt] = sy() - y(0)] [L[u(t) = 1/*]]