Suppose that a fourth order differential equation has a solution $y = -2 e^{4 x} x \cos(x)$.

(a) Find such a differential equation, assuming it is homogeneous and has constant coefficients.
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(b) Find the general solution to this differential equation. In your answer, use $c_1, c_2, c_3$ and $c_4$ to denote arbitrary constants and $x$ the independent variable. Enter $c_1$ as c1, $c_2$ as c2, etc.
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