For each of the following boundary conditions determine if i

For each of the following boundary conditions, determine if it Is linear or not linear and if it is homogeneous or non-homogeneous (circle your answer): partial differential u/partial differential x (0, t) = u^6(L, t) Linear: Yes/No, Homogeneous: Yes/No. partial differential u/partial differential x (0, t) = 0 Linear: Yes/No, Homogeneous: Yes/No. partial differential u/partial differential x (0, t) = u(L, t) Linear: Yes/No, Homogeneous: Yes/No. partial differential u/partial differential x (0, t) = sin(t) Linear: Yes/No, Homogeneous: Yes/No. partial differential u/partial differential x (0, t) = u + 53 Linear: Yes/No, Homogeneous: Yes/No. partial differential u/partial differential x (0, t) = t + 5 Linear: Yes/No, Homogeneous: Yes/No.

Solution

(a) Non-linear because in Right side U^6

(b) Homogenious because right side is zero

(c) Linear beause all power of U is one and degree is one

(d) linear beause all power of U is one and degree is one

(e) linear beause all power of U is one and degree is one

(f) linear beause all power of U is one