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I have a simple question,

There are some functions $f(t)$, $g(t)$ and lets say $F(s)$ and $G(s)$ for the form of Laplace transform of $f(t)$ and $g(t)$, respectively.

While I am solving differential equation with Laplace Transform,

I got this relationship

$$F(s)=\frac{f(0)}{s + G(s)}$$

how can I solve in terms of $f(t)$?

I looked up the convolution theorem but it is not a form of $f(t)*g(t)$

please help me

Thanks in advance

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  • $\begingroup$ Without knowing the form of $G$ the best you can do is the inverse Laplace transform. $\endgroup$
    – copper.hat
    Mar 24, 2015 at 22:12
  • $\begingroup$ how to inverse Laplace transform of F(s)? can I write it just like this ? $\endgroup$
    – eric
    Mar 24, 2015 at 22:18
  • $\begingroup$ $$f(t)=f(0)*e^{-K(s)t}$$ $\endgroup$
    – eric
    Mar 24, 2015 at 22:18
  • $\begingroup$ No. It is not that simple. $\endgroup$
    – copper.hat
    Mar 24, 2015 at 22:19
  • $\begingroup$ could you give me some hints or could you show me the some steps ? $\endgroup$
    – eric
    Mar 24, 2015 at 22:20

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