Mathematics Homework Solutions
Problem
#70561

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

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question.doc
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.

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