-(2xy')'+ry= = Xy,
for x E [1,2].
Is this a Sturm-Liouville problem? If so, explain why and decide whether it is regular
or singular. If not, explain why not.
(b) Suppose the boundary conditions were replaced by
y(1) = 0,
y(2) - y (1) = 0.
Would this be a Sturm-Liouville problem? Explain your answer.
2. Consider the BVP
y(0) = 0,
y(1) = 0.
(a) Find the associated Sturm-Liouville eigenvalue problem.
(b) Find the eigenvalues and eigenfunctions.
(c) Solve the BVP using an eigenfunction expansion.
(d) Optional (not for marks): Solve the BVP directly and plot both solutions on the same
Hint: Pay careful attention to all signs.
3. Consider the integral equation
(a) What type of integral equation is this? State both the name and whether it is of the
first or second kind.
1 of 2
(b) Suppose that
l. 0 (x +
for l1 # À2. Find (211,u2). Make sure to clearly justify your answer.
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