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Partial Differential Equation Solution

1. Consider the partial differential equation:
q(x) u/t = /x (p(x) u/x)
(a) Confirm that
U(x) = A + (B-A)(integral from 0 to x (p(s)^-1 ds))/(integral from 0 to L (p(s)^-1 ds))
Is a solution of the partial differential equation
(b) Confirm that if u=U+v then v indeed satisfies the partial diff eq if u does
(c) Confirm that X(x)T(t) is indeed a solution of the partial diff eq if X and T are solutions of the following respectively:
d/dx (p(x) dX/dx) - kq(x)X = 0
dT/dt = kT
where k is a constant


Solution Summary

A PDE is solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.