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Integral equation with a derivative of the function inside the integral

$$f(x) = 2\int_{0}^{t} sin(8u)f'(t-u) du + 8sin(8t) , t\geq 0$$
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

$$s^{2} F(s) + 64F(s)- 16(F(s) - f(0)) =64$$
and i havent been given f(0)
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