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## Homework Statement

A first-order dynamic system is represented by the differential equation,

[tex]5\frac{dx(t)}{dt} + x(t) = u(t).[/tex]

Find the corresponding transfer function and state space reprsentation.

## Homework Equations

## The Attempt at a Solution

Putting the equation in the Laplace domain yields,

[tex]5sX(s) + X(s) = U(s)[/tex]

[tex]\Rightarrow G(s) = \frac{X(s)}{U(s)} = \frac{1}{1+5s}[/tex]

For the state space equations,

[tex]\frac{dx(t)}{dt} = -0.2x(t) + 0.2u(t)[/tex]

The answer they provide is,

[tex]\frac{dx(t)}{dt} = -0.2x(t) + 0.5u(t), \quad y(t) = 0.4x(t)[/tex]

How did they 0.5u(t) and how did they know that y(t) = 0.4x(t)?

Thanks again!