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Problem: Find the adjoint operator and its domain for:

a) . (Assume is continuously differentiable and is continuous on the interval .

This is the answer, I just need to see the steps to arrive there:

, with boundary conditions .

b)

Again, here is the answer, but I need to see the solution method:

#### Solution Preview

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Problem: Find the adjoint operator and its domain for:

a) . (Assume is continuously differentiable and is continuous on the interval .

This is the answer, I just need to see the steps to arrive there:

, with boundary conditions .

Solution. By definition of the adjoint operator L, we have
(1)
Now we integrate by parts, we have

...

#### Solution Summary

Adjoint operators are found. The solution is detailed and well presented.

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