Quick question about solving an eigenvalue problem

[Hakkinen]

I just have a question about the problem for when the eigenvalue = 0

Homework Statement

for y_{xx}=-\lambda y with BC y(0)=0 , y'(0)=y'(1)

Homework Equations

The Attempt at a Solution

y for lamda = 0 is ax+b
so from BC:
y(0)=b=0

and a=a

What is the conclusion to make from this? lamda = 0 and the eigenfunction is constant?

 

[Dick]

I just have a question about the problem for when the eigenvalue = 0

Homework Statement

for y_{xx}=-\lambda y with BC y(0)=0 , y'(0)=y'(1)

Homework Equations

The Attempt at a Solution

y for lamda = 0 is ax+b
so from BC:
y(0)=b=0

and a=a

What is the conclusion to make from this? lamda = 0 and the eigenfunction is constant?

I think the conclusion is just that y(x)=ax. That doesn't make it constant.

 

[Hakkinen]

I think the conclusion is just that y(x)=ax. That doesn't make it constant.

Thanks for the reply. So the eigenvalue is 0 and the eigenfunction is just ax, with a determined by some IV?

 

[Dick]

Thanks for the reply. So the eigenvalue is 0 and the eigenfunction is just ax, with a determined by some IV?

Well, you don't conclude that the eigenvalue is 0, you were given that, right? And, yes, you can conclude that y(x)=ax. You can't determine a from the conditions you are given. Another IV would do it.