Please explain this sentence.
"The importance of homogeneity is the scale invariance of the functions. Which implies that the graphs of the functions will be scale invariant."
subject is about homogeneous functions.
what is the interpretation of homogeneity in differential equations?
Your quote comes from the first answer in What Does Homogenisation Of An Equation Actually Mean?. I think the meaning of the sentence was explained by "In other words, any point that satisfies the equation immediately implies the entire ray going through that point and the origin of the space belong to the geometrical object." This can be called scale invariant also. For differential equations, they can be transformed into the form $0 = T(f)(x)$ where $T$ is a differential operator. In many important cases, the operator is homogeneous and therefore the equation is called a homogeneous differential equation. There are many important non-homogeneous equations also.
