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Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.

3 votes
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Solving a integro-differential equation

I am trying to solve an integro-differential equation: $$ {\frac{d}{dt}} f(t)=\int_0^t k(t-\tau)S(\tau)f(\tau) d\tau $$ with initial condition $f(0)=1$ If $k(t)=c\delta(t)$ with $c$ being constant, …