Classify the following PDEs and boundary or initial conditio

Classify the following PDEs and boundary or initial conditions as homogeneous or non-homogeneous. If nonhomogeneous, state why. delta u/delta t - k delta^2 u/delta x^2 = delta u/delta x

Solution

A linear partial differential equation is non-homogeneous if it contains a term that does not depend on the dependent variable.

If all the terms of a PDE contain the dependent variable or its partial derivatives then such a PDE is called non-homogeneous partial differential equation.

Therefore, (a) is homogeneous and (b), (c) is non-homogeneous.

The boundary conditions are non-homogeneous as homogeneous boundary conditions looks like

u|_x=0 = u|_x=L = 0