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?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Laplace transform: function defined by parts

Loading...

Similar Threads for Laplace transform function | Date |
---|---|

A Inverse Laplace transform of a piecewise defined function | Feb 17, 2017 |

A Initial value ODE with shifting forcing function | Jul 21, 2016 |

Inverse Discrete Laplace Transform | May 28, 2015 |

Laplace transform with Heaviside function | Jun 18, 2014 |

Inverse Laplace Transform of a product of exponential functions | Aug 28, 2013 |

**Physics Forums - The Fusion of Science and Community**