Fourier Transforms & Partial Diff Eqns

[Firepanda]

Basically I have a question (2nd Screenshot) which I am trying to mirror with the below example, which has a written solution.

What I can't work out is how the solutions would differ given the boundary conditions, where would I put them in? Are the soutions to both problems the same?

Here is the worked example: http://i40.tinypic.com/3509kw2.png

Here is the new question: http://i41.tinypic.com/fn8c9t.png

(I would put them directly into this thread as images, but I don't know the resolution of peoples monitors and if they would scale ok)

Thanks

 

[lippyka]

The solutions to the two questions may be different. In the first question, the boundary conditions specify that the function must take the form of a polynomial of degree 3 or less, which means that the solution must be of the form f(x) = ax^3 + bx^2 + cx + d. For the second question, the boundary conditions specify that the function must take the form of a polynomial of degree 4 or less, which means that the solution must be of the form f(x) = ax^4 + bx^3 + cx^2 + dx + e.