Green's Function Exercise

Question

y = f(x), y(0) = y(1) = 0, where L(y) = y" + y

Hint:
1. G(x, ε) = c1 u(x), x < ε and c2 v(x), x > ε
2. Find u(x) -> u(0) = 0 and v(x) -> v(1) = 0
3. y" + y = 0, y = acos(x) + bsin(x)
4. Find u(x) satisfies u" + u = 0, u(0) = 0 and v(x) satisfies v" + v = 0, v(1) = 0
5. Then, go back to write the Green's function

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