What is the solution for y^{'''}+4y^{''}-16y^'-64y=0 ?

The solution for y^{'''}+4y^{''}-16y^'-64y=0 is y=c_{1}e^{4t}+c_{2}e^{-4t}+c_{3}te^{-4t}

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y^{'''}+4y^{''}-16y^'-64y=0

y^{^{'''}} + 4 y^{^{''}} - 16 y^{^{'}} - 64 y = 0

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

Solution steps

y^{'''} (t) + 4 y^{''} (t) - 16 y^{'} (t) - 64 y = 0

Solve linear ODE:

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

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

What is the solution for y^{'''}+4y^{''}-16y^'-64y=0 ?
The solution for y^{'''}+4y^{''}-16y^'-64y=0 is y=c_{1}e^{4t}+c_{2}e^{-4t}+c_{3}te^{-4t}