# If linearity follows from homogeneity and additivity why do non-homogenous systems of linear equations exist?

According to this wikipedia page, Linear Maps or Linear Functions satisfy properties of homogeneity and additivity. (Later on in the paragraph they also talk about how this can be extended for linear operators like derivative or differential)

At the same time, the definition of non-homogenous linear ODE (of first order) is: $$y\ '$$ + $$p(x)y$$ = $$r(x)$$ where $$r(x)$$ $$\neq$$ $$0$$

Why is there a mismatch in the definition of Linearity?

• Why do non-homogeneous systems of linear equations exist? May 15, 2020 at 9:13
• Thanks for the suggestion. May 15, 2020 at 9:32