What is the solution for y^{'''}-y^{''}-8y^'+12y=0 ?

The solution for y^{'''}-y^{''}-8y^'+12y=0 is y=c_{1}e^{-3t}+c_{2}e^{2t}+c_{3}te^{2t}

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y^{'''}-y^{''}-8y^'+12y=0

y^{^{'''}} - y^{^{''}} - 8 y^{^{'}} + 12 y = 0

y = c_{1} e^{- 3 t} + c_{2} e^{2 t} + c_{3} t e^{2 t}

Solution steps

y^{'''} (t) - y^{''} (t) - 8 y^{'} (t) + 12 y = 0

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{2 t} + c_{3} t e^{2 t}

y = c_{1} e^{- 3 t} + c_{2} e^{2 t} + c_{3} t e^{2 t}

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What is the solution for y^{'''}-y^{''}-8y^'+12y=0 ?
The solution for y^{'''}-y^{''}-8y^'+12y=0 is y=c_{1}e^{-3t}+c_{2}e^{2t}+c_{3}te^{2t}