[tex] f(x) = 2\int_{0}^{t} sin(8u)f'(t-u) du + 8sin(8t) , t\geq 0 [/tex](adsbygoogle = window.adsbygoogle || []).push({});

is this problem solvable? i've never seen an integral equation like this with an f'(t-u)

i tried to solve it us the convolution theorem and laplace transforms but ended up with

[tex] s^{2} F(s) + 64F(s)- 16(F(s) - f(0)) =64 [/tex]

and i havent been given f(0)

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# Integral equation with a derivative of the function inside the integral

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