For the following ODEs, (i) determine whether they are initial value problems or boundary value problems, (ii) find the solution, (iii) state whether the solution is unique.
(a) \frac{d^2y}{dx^2} + 6\frac{dy}{dx} - 7y = 0, \qquad y(0) = 4, \quad y'(0) = 7,
(b) \frac{d^2y}{dx^2} + 4y = 0, \qquad y(0) = -2, \quad y(2\pi) = -2,
(c) \frac{d^2y}{dx^2} - 2\frac{dy}{dx} + y = 0, \qquad y(0) = -5, \quad y(2) = 2e^{-2}.
