A rod along with both ends insulated has steady temperature obeying with

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Linear algebra and vector spaces · Ordinary differential equations

Conditions of Validity, Ch Inner products, orthogonality and the adjoint

Problem

A rod along

[0,1]

with both ends insulated has steady temperature

u

obeying

-u''=f

with

u'(0)=u'(1)=0

, where the heat source is

f(x)=3x^2-a

for a constant

a

. ((a)) Using

\mathcal{N}(T^{\dagger})

for this operator and domain, find the one value of

a

for which a solution exists. ((b)) For that value, find every solution

u

, and say which feature of

\mathcal{N}(T^{\dagger})

the free part of your answer reflects.

Related theory

Ordinary differential equations

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