Two-Point Boundary Value Problem

[Jamin2112]

Homework Statement

y'' + ßy = 0, y'(0)=0, y'(L)=0

Homework Equations

Meh

The Attempt at a Solution

I so already did the ß>1 and ß<1; I'm stuck on the ß=0. It seems easy enough. y'' = 0 -----> y' = A -----> 0=A, 0=A (from the two initial conditions) ------> No non-trivial solution.

But...

The answer in the back of the book says ß₀=0, y₀(x)=1; ...


??

 

[LCKurtz]

Homework Statement

y'' + ßy = 0, y'(0)=0, y'(L)=0

Homework Equations

Meh

The Attempt at a Solution

I so already did the ß>1 and ß<1; I'm stuck on the ß=0. It seems easy enough. y'' = 0 -----> y' = A -----> 0=A, 0=A (from the two initial conditions) ------> No non-trivial solution.

Starting with y'' = 0 you need to integrate twice to get y, getting two constants.

 

[Jamin2112]

Starting with y'' = 0 you need to integrate twice to get y, getting two constants.

The boundaries it gives me are in terms of y'


Of course I know
y'' = 0 -----> y' = B ----> y = Ax + b

 

[LCKurtz]

The boundaries it gives me are in terms of y'


Of course I know
y'' = 0 -----> y' = B ----> y = Ax + b

But the point is: does your boundary condition force only the trivial solution or can you get a non-trivial solution in this case?