Find the general solution of this differential equation. $\displaystyle \frac{{{d}^{{2}}{y}}}{{{\left.{d}{t}\right.}^{{2}}}}+{12}\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}+{35}{y}={5}{t}^{{2}}-{4}+{4}{e}^{{-{9}{t}}}$ Because the solution is of the form $\displaystyle {k}_{{1}}{y}_{{1}}{\left({t}\right)}+{k}_{{2}}{y}_{{2}}{\left({t}\right)}+{y}_{{p}}{\left({t}\right)}$ , please use $\displaystyle {C}$ and $\displaystyle {D}$ as the arbitrary constants. NOTE: If your first answer does not work, you should try switching the $\displaystyle {C}$ & $\displaystyle {D}$ to the alternate solutions of the homogeneous equation.