Consider the heat equation
.
satisfies the ordinary differential equation
).
Show that
then
, 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
#45886
Differential Equations : Solution to Heat Equation
Consider the heat equation
.
Show that if where and is a constant, then satisfies the ordinary differential equation
, (where ).
Show that
=
is independent of only if . Further, show that if then
where C is an arbitrary constant. From this last ordinary differential equation, and assuming , deduce that
is a solution of the heat equation (here A is an arbitrary constant).
Show that as tends to zero from above,
for
and that for all
where B is a (finite) constant.
Given that , find B. What physical and/or probabilistic interpretation might one give to
A heat equation is investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.
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