Suppose that the characteristic equation for a differential equation is $(r-2)^2 (r-4)^2 = 0$.

(a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. Enter your answer using $y, y^{\,\prime}, y^{\,\prime\prime}, y^{\,\prime\prime\prime}, y^{\,\prime\prime\prime\prime}$ for the dependent variable and its derivatives.
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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, use $y$ for the dependent variable, and use $x$ for the independent variable. Enter $c_1$ as c1, $c_2$ as c2, etc.
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