Ordinary Differential Equations – Writing Piecewise Functions in Terms of Unit Step Functions

Question

Write the piecewise function

$f(t) = \begin{cases}
2t, & 0\leq t < 3 \\
6, & 3 \le t < 5 \\
2t, & t \ge 5 \\
\end{cases}
$

in terms of unit step functions.

So here is what i;ve got just guessing , I don't think i'm correct. I really need some help. But I got:

$f(t) = 2t[u(t-0) – u(t-3)] + 6[u(t-3) – u(t-5)] + 2t[u(t-5) – u(t – \infty)]$

Which becomes

$f(t) = 2t[u(t) – u(t-3)] + 6[u(t-3) – u(t-5)] + 2t[u(t-5)]$

Answer 1

Solution is correct, verified by teacher.

$f(t) = 2t[u(t) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5)]$