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## Homework Statement

I have to find the eigenvalues&function of the eqn:

[tex]y''+\lambda y =0[/tex]

With the boundary conditions:

[tex]y(0)+y'(0) = 0[/tex] and [tex]y(\pi) =0[/tex]

## Homework Equations

## The Attempt at a Solution

I get the general equations, okay, but am having trouble due to the boundary conditions.

Assuming [tex]\lambda>0[/tex], then get the general solution:

[tex]y(x)=A\sin(x\sqrt{\lambda})+B\cos(x\sqrt{\lambda})[/tex]

The best i can do now is that:

[tex]y(\pi)=A\sin(\sqrt{\lambda}\pi)+B\cos(\sqrt{\lambda}\pi)=0[/tex]

Which can only be valid if B = 0 and [tex]\sqrt{\lambda} = n[/tex] where n is a positive integer.

Now I run into problems, the second bc gives:

[tex]y(0)=A\sin(n 0)=0[/tex]

[tex]y'(0)=nA\cos( n 0)=nA[/tex]

So:

[tex]y(0)+y'(0) = 0 + nA = 0[/tex]

Am I on the right track, or can anyone see where I am messing up?

Thanks.