Pregunta: y'' + 2y' − 8y = 6e^(−2x) − e^(−x), y(0)=1, y'(0)=0 y(x)=? solve by variation of parameters

Given differential equation is $\mathrm{y}{}^{″}+2{\mathrm{y}}^{\prime }-8\mathrm{y}=6{\mathrm{e}}^{-2\mathrm{x}}-{\mathrm{e}}^{-\mathrm{x}},\mathrm{y}\left(0\right)=1,{\mathrm{y}}^{\prime }\left(0\right)=0.$

Using variation of parameter method;

The corresponding homogeneous equ...