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- Homework Statement
- Let f be a continuous function in a interval I containing the origin and let

##y = y(x) = \int_0^x sin(x - t)f(t) dt##

Prove that ##y'' + y = f(x)## and ##y(0) = y'(0) = 0## for all x ##\in I##

- Relevant Equations
- ...

I know how to solve ##\frac{d}{dx} \int_0^{x^2} sin(t^2) dt## and from the statement I got that f(0) = 0 because f contains the origin and is continuous.

I tried y'(x) = sin(x - x)f(x) - sin(x - 0)f(0) but that doesn't seem to look good.

I tried y'(x) = sin(x - x)f(x) - sin(x - 0)f(0) but that doesn't seem to look good.