In this exercise you will solve the initial value problem
y''-8 y' +16 y =\frac{e^{-4x}}{1+x^{2}},\ \ y(0) = 2,\ \ y'(0) = -7.

(1) Let

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NOTE: The order in which you enter the answers is important; that is,
C_1 f(x) + C_2 g(x) \neq C_1 g(x) + C_2 f(x).
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(2) The particular solution

(3) The most general solution to the non-homogeneous differential equation

You can earn partial credit on this problem.