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

Hey! I have tried to solve this problem but I get stuck when it comes to the inverstransforming. Anyway here is the problem and my attempt to a solution:

Solve [tex]f(t)=2\int_{0}^{t}sin(9u)f'(t-u)du+sin9t,t\geq 0[/tex] for f(t)

3. The attempt at a solution

Laplacetransforming:

[tex]F(s)=\frac{18}{s^{2}+9^{2}}sF(s) + \frac{9}{s^{2}+9^{2}}[/tex]

Solving F(s)

[tex]F(s)=\frac{9}{s^{2}+9^{2}-18s}[/tex]

I dont know what to do now, with the inverstransform? And the F(s) feels wrong..Is my Laplacetransforming correct, I have tried to use the convolution theorem..but I dont know if I used it correct..

Thanks!

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# Laplacetransform an Integral, problem with the inverstransform!

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