For each of the following boundary conditions, determine if it Is linear or not

Question

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.

Explanation / Answer

(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

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