- #1
libelec
- 176
- 0
I have this DE:
[tex]\[y'' - 4y' + 8y = f(t) = \left\{ \begin{array}{l}
t{\rm{ }},t \in [0,2) \\
t + 1{\rm{ }},t \in [2,4) \\
0{\rm{ }},t \ge 4 \\
\end{array} \right.\]
[/tex]
I have problems transforming f(t). I know that when I have a function defined by parts, I have to use the translation theorem. But for t > 4, f(t) = 0 would let me something like [tex]\[f(t) = t.H(t) + 1.H(t + 2) + 0.H(t + 4)\]
[/tex], the 3rd term being irrelevant.
What am I doing wrong?
[tex]\[y'' - 4y' + 8y = f(t) = \left\{ \begin{array}{l}
t{\rm{ }},t \in [0,2) \\
t + 1{\rm{ }},t \in [2,4) \\
0{\rm{ }},t \ge 4 \\
\end{array} \right.\]
[/tex]
I have problems transforming f(t). I know that when I have a function defined by parts, I have to use the translation theorem. But for t > 4, f(t) = 0 would let me something like [tex]\[f(t) = t.H(t) + 1.H(t + 2) + 0.H(t + 4)\]
[/tex], the 3rd term being irrelevant.
What am I doing wrong?