Pregunta: Solve the given initial-value problem. y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) = 1/2 , y'(0) = 5/2 , y''(0) = − 5/2

Given data,
The given initial-value problem. $\mathrm{y}{}^{‴}-2\mathrm{y}{}^{″}+{\mathrm{y}}^{\prime }=2-24{\mathrm{e}}^{\mathrm{x}}+40{\mathrm{e}}^{5\mathrm{x}}$, $\mathrm{y}\left(0\right)=\frac{1}{2},{\mathrm{y}}^{\prime }\left(0\right)=\frac{5}{2},\mathrm{y}{}^{″}\left(0\right)=-\frac{5}{2}$.
Find the characteristic equation associated with the...