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## Main Question or Discussion Point

"A PDE satisfied by a suitably differentiable function u of the independent variables x1, ... ,xn, is said to be linear if u and its partial derivatives only occur linearly and, posibly, with coefficients that are functions of independent variables. This PDE may, or may not, contain a function f that depends only on the independent variables. The PDE is said to be homogeneous when the function f(x1,...,xn) = 0; otherwise it is nonhomogeneous."

Is there a pictorial way to expound on this for me?

Is there a pictorial way to expound on this for me?