What is the solution for y^{'''}+8y^{''}-12y^'-144y=0 ?

The solution for y^{'''}+8y^{''}-12y^'-144y=0 is y=c_{1}e^{4t}+c_{2}e^{-6t}+c_{3}te^{-6t}

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y^{'''}+8y^{''}-12y^'-144y=0

y^{^{'''}} + 8 y^{^{''}} - 12 y^{^{'}} - 144 y = 0

y = c_{1} e^{4 t} + c_{2} e^{- 6 t} + c_{3} t e^{- 6 t}

Solution steps

y^{'''} (t) + 8 y^{''} (t) - 12 y^{'} (t) - 144 y = 0

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 6 t} + c_{3} t e^{- 6 t}

y = c_{1} e^{4 t} + c_{2} e^{- 6 t} + c_{3} t e^{- 6 t}

What is the solution for y^{'''}+8y^{''}-12y^'-144y=0 ?
The solution for y^{'''}+8y^{''}-12y^'-144y=0 is y=c_{1}e^{4t}+c_{2}e^{-6t}+c_{3}te^{-6t}