TITLE: Let $f(x)=\sin(x)-\int_{0}^{x}{(x-u)f(u)du}$ where $f(x)$ is continuous. Find $f(x)$.
QUESTION [3 upvotes]: Let $$f(x)=\sin(x)-\int_{0}^{x}{(x-u)f(u)du}$$ where $f(x)$ is continuous. Find $f(x)$. 
Initially, I use FTC and obtain $f(x)=\sin(x)$ but in the question didn't mention $f$ is differentiable. Then I get stuck for half an hour. Can anyone guide me ?

REPLY [4 votes]: Hint: Another approach in which you can find the final solution sis to use the Laplace Transformation. Take LT form the both sides of OE and note that there is a convolution form in $$\int_{0}^{x}{(x-u)f(u)du}=t*f(x)$$
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