working on a physical problem I arrived at the following equation $$ y(x) + A \int_{0}^{x} e^{\lambda (t-x)} y(t) \mathrm{d}t = 0$$ and after some struggling (not that easy to apply the basic Laplace transform tecnique) I had a look on EqWorld, where I discover that the equation $$y(x) + A \int_{0}^{x} e^{\lambda(x-t)}y(t)\mathrm{d}t = f(x)$$ has solution $$y(x) = f(x) - A \int_{0}^{x} e^{(\lambda-A)(x-t)} f(t)\mathrm{d}t$$ So, my equation being a particular case of the latter for f=0, I am lead to the conclusion only the nihil solution satisfies my equation, which is physically bizarre.Any hints here please?
2026-03-28 13:29:45.1774704585
Integral Equation without solution?
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