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Freebase(0.00 / 0 votes)Rate this definition: Homogeneity. In general, homogeneity is defined as the quality or state of being homogeneous. It also means having a uniform structure throughout. For instance, a uniform electric field would be compatible with homogeneity.
add a comment |. up vote 0 down vote. The simplest test of homogeneity, and definition at the same time, not only for differential equations, is the following: An equation is homogeneous if whenever $\varphi$ is a solution and $\lambda$ scalar, then $\lambda\varphi$ is a solution as well.share | cite | improve this answer.dd a comment |. up vote 0 down vote. The simplest test of homogeneity, and definition at the same time, not only for differential equations, is the following: An equation is homogeneous if whenever $\varphi$ is a solution and $\lambda$ scalar, then $\lambda\varphi$ is a solution as well.