y" - 3y + 2y = f(x). (a) Suppose that in Eq.(2), f(x) = 0. (i) Write down the order and degree of the equation, then find two values of a so that y = ez is a solution of the equation. (ii) Write the differential equation as a system of first-order differential equations, then use the eigenvalue method to find the general solution of the system. (b) Suppose that in Eq.(2), f(x) = 4x. Use the method of undetermined coefficients to find a general solution for the equation. How many conditions are needed to find a particular solution for this equation?

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