Consider the Voltera integral equation: $$ψ(x)=e^{-x}\cos(x)-\int_{0}^{x}e^{-(x-t)}\cos(x)ψ(t)dt$$
How can I solve this equation by converting it to a differential equation? The solution is $$\psi(x)=\frac{\cos(x)}{e^{x+\sin(x)}}$$ I mean $$\psi(x)=\cos(x)e^{-(x+\sin(x))}$$