Is there any method to solve the following integral equation, either analytically or numerically:
$$A(t) cos(\omega t) + \int_0^t \omega A(\tau) sin(\omega \tau) d\tau = f(t)$$
Where: $$A(t): unknown\ function\ which\ must\ be\ found$$ $$\omega: angular\ frequency\,\ an\ arbitrary\ positive\ value$$ $$t: time$$ $$f(t): known\ function$$
Differentiate, you get a differential equation:
$$ A'(t) \cos \omega t - \omega A(t) \sin \omega t = \omega A(t) \sin \omega t + f'(t) $$
Linear, first order, thus solvable.