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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: $$A(t): unknown\ function\ which\ must\ be\ found$$ $$\omega: angular\ frequency\,\ an\ arbitrary\ positive\ value$$ $$t: time$$ $$f(t): known\ function$$

Pirooz
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1 Answers1

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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.

vonbrand
  • 27,812
  • Yes, you are right. But I think you have made a mistake while differentiating. Sine terms cancel each other. – Pirooz Apr 21 '20 at 05:27