I have this DE:(adsbygoogle = window.adsbygoogle || []).push({});

[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?

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# Laplace transform: function defined by parts

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