i'm struggling to understand the difference between inhomogeneous and homogeneous, for example if i was to solve the following Pde
$$100\frac{\partial^2 u}{\partial x^2}=\frac{\partial u}{\partial t}, 0<x<1,t>0$$ with conditions $u(0,t)=0,t>0$,$u(1,t)=0,t>0$ $u(x,0)=\sin(2\pi x)-\sin(5\pi x),0\le x\le 1$ I know these conditions are homogeneous. However if i was to consider the next PDE $$\frac{\partial u}{\partial t}=2\frac{\partial^2 u}{\partial x^2}$$ with boundary conditions $u(0,t)=5,t>0$, $u(\pi,t)=10,t>0$, $u(x,0)=6,0<x<\pi$
I don't understand why these conditions are inhomeogenous. I was wondering if anyone could explain why. I have already Solved these Pde's just going along with the fact that the conditions are inhomeogenous for the second one.