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This paper extends our previous works arXiv:1802.07306 [math.NT],arXiv:1808.02382 [math.NT] on determining the spectrum, in the Berkovich sense,of ultrametric linear differential equations. Our previous works focused onequations with constant coefficients or over a field of formal power series. Inthis paper, we investigate the spectrum of $p$-adic differential equations at ageneric point on a quasi-smooth curve. This analysis allows us to establish asignificant connection between the spectrum and the spectral radii ofconvergence of a differential equation when considering the affine line.Furthermore, the spectrum offers a more detailed decomposition compared toRobba's decomposition based on spectral radii.

Spectrum of p-adic linear differential equations I: The shape of the spectrum