Classify the following PDEs and companion boundary condition

Classify the following PDEs and companion boundary conditions as linear or nonlinear. If linear, specify if the PDE is homogeneous or non homogeneous. u_t = u_xx, u(0) = 0, u_x (L) = 0 u_t = u_xx - x^2u, u(0) = 0, u(L) = 0 u_t = u_xx - x^2, u(0) = 0, u(L) = 0. u_t = u_xx + u, u_x (0) = 0, u_x(L) = 0 u_t = u_xx, u + u_x (0) = 0, u - u_x (L) = 0.

Solution

a.) Linear and homogeneous

b.) Non linear

c.) Linear, non homogeneous

d.) Linear homogeneous

e.) Non Linear

f.) Linear