$30.[\frac{0\mathrm{.}08}{0\mathrm{.}43}$ Points$]$ DETAILS PREVIOUS ANSWERS ZILLDIFFEQ$912\mathrm{.}1\mathrm{.}012.MY$ NOTES ASK YOUR TEACHER Use separation $of$ variables $to$ find, $if$ possible, product solutions for the given partial differential equation. $(Use$ the separation constant $-1.If$ not possible, enter IMPOSSIBLE.$)a2a^{2}u-a^{2}u+2kkoa{x}^{2}at2at2=0u(x,t)=(6+ce2kt)(cz+(24)$ Ige $(3)$ tegelt legal$-x+ve+ve+a?)itxel-VP+d?$