Question

How do I approach this?

*58. a) If g is a given function which is continuous and positive on the interval (0, L], show that the only solution of the boundary value problem y' – g(x)y = 0; y(0) = 0, y(L) = 0, L>0, is y = 0. (Hint: If y = 0, then y achieves its maximum or minimum value at some point to where 0 < 0 < L.] b) Find all possible such that there is a solution of y"' + 2y' + 2ly = 0) with y(0) = y(L) = () and y not identically zero.

Answer 1

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