Consider the heat equation
.
satisfies the ordinary differential equation
).
(b) Show that
.
then
where C is an arbitrary constant.
, deduce that
is a solution of the heat equation (here A is an arbitrary constant).
tends to zero from above,
where B is a (finite) constant.
Mathematics Homework Solutions
#93783
Heat Equations
Consider the heat equation
.
(a) Show that if where and is a constant, then satisfies the ordinary differential equation
, (where ).
(b) Show that
=
is independent of only if .
(c) Further, show that if then
where C is an arbitrary constant.
(d) From this last ordinary differential equation, and assuming , deduce that
is a solution of the heat equation (here A is an arbitrary constant).
(e) Show that as tends to zero from above,
for
and that for all
where B is a (finite) constant.
Please see the attached file for the fully formatted problems.
A heat equation is investigated. The solution is detailed and well presented.
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