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}

\frac{d}{d x} (5 cos (x) - cos (5 x))

\int \frac{3 x ^{2} - x + 1}{x ^{3} - x ^{2}} d x

y^{^{''}} + 49 y = cos (10 t)

ln (x^{3} + 5 x + 3)

x \to 1 lim (x sin (\frac{1}{x}))

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}