(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]y(x) = e^{3x} + \int_0^{x}\hspace{1mm}y(t)\hspace{1mm}e^{x-t}\hspace{1mm}dt[/tex]

2. Relevant equations

[tex](f*g)(x) = \int_0^{x}\hspace{1mm}y(t)\hspace{1mm}g(x-t)\hspace{1mm}dt[/tex]

[tex]L(f*g;s) = L(f;s)L(g;s)[/tex]

I will use [tex]Y(s)[/tex] to denote [tex]L(y;s)[/tex]

3. The attempt at a solution

I tried to solve this like all the other problems I have encountered so far, I took the laplace transform of both sides, giving:

[tex]Y(s) = s-3 + (s-1)Y(s)[/tex]

Which gave me:

[tex]Y(s) = -\frac{s-3}{s-2}[/tex]

However, this doesn't work out, as far as I'm aware there is no inversion for 1 ( I have only dealt with the standard Laplace transforms and can only invert back to them ).

The book I have gives:

[tex]Y(s) = \frac{s-1}{(s-2)(s-3)}[/tex]

But I'm not sure how this was calculated, I'll appreciate any hints and pointing out where I have gone wrong, thanks.

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# Homework Help: Solving Integral Equation with Laplace Transform

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