Respuesta :

LammettHash
[tex]y'''+2y''-4y'-8y=0[/tex]

has characteristic equation

[tex]r^3+2r^2-4r-8=r^2(r+2)-4(r+2)=(r^2-4)(r+2)=(r-2)(r+2)^2=0[/tex]

which has roots at [tex]r=\pm2[/tex]. The negative root has multiplicity 2. So the general solution is

[tex]y=C_1e^{2x}+C_2e^{-2x}+C_3xe^{-2x}[/tex]

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