Pregunta: Solve the given initial-value problem. y′′′ + 18y′′ + 81y′ = 0, y(0) = 0, y′(0) = 1, y′′(0) = −8

Consider the provided differential equation $\mathrm{y}{}^{‴}+18\mathrm{y}{}^{″}+81{\mathrm{y}}^{\prime }=0$ where $\mathrm{y}\left(0\right)=0,{\mathrm{y}}^{\prime }\left(0\right)=1,\mathrm{y}{}^{″}\left(0\right)=-8$ .

The auxiliary equation of $\mathrm{y}{}^{‴}+18\mathrm{y}{}^{″}+81{\mathrm{y}}^{\prime }=0$ is ${\mathrm{m}}^3+18{\mathrm{m}}^2+81\mathrm{m}=0$ .

Here, $\mathrm{m}({\mathrm{m}}^2+18\mathrm{m}+81)=0$ can be ...