Write the auxiliary equation needed to annihilate the given equation in terms of the differential operator D. Write the equation in it's fully factored form:

 $\displaystyle {y}{''}+{81}{y}={3}{x}+{e}^{{{2}{x}}}$ 

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Write the general solution to the differential equation in the form $\displaystyle {y}={y}_{{c}}+{y}_{{p}}$ in terms of the co-efficients $\displaystyle {c}_{{1}},{c}_{{2}},\ldots$  (Do not solve for $\displaystyle {y}_{{p}}$ !!). Write your solutions in the standard order (polynomials, exponential, cos(x), sin(x)).

Preview Question 6 Part 2 of 2