What is the solution for y^{'''}+5y^{''}-y^'-5y=0 ?

The solution for y^{'''}+5y^{''}-y^'-5y=0 is y=c_{1}e^{-5t}+c_{2}e^{-t}+c_{3}e^t

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y^{'''}+5y^{''}-y^'-5y=0

y^{^{'''}} + 5 y^{^{''}} - y^{^{'}} - 5 y = 0

y = c_{1} e^{- 5 t} + c_{2} e^{- t} + c_{3} e^{t}

Solution steps

y^{'''} (t) + 5 y^{''} (t) - y^{'} (t) - 5 y = 0

Solve linear ODE:

y = c_{1} e^{- 5 t} + c_{2} e^{- t} + c_{3} e^{t}

y = c_{1} e^{- 5 t} + c_{2} e^{- t} + c_{3} e^{t}

y^{^{''}} + 2 y^{^{'}} = 3 y

y^{^{'''}} + 7 y^{^{''}} - 5 y^{^{'}} - 75 y = 0

y^{^{''}} + 256 y = 0

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 3

\frac{d ^{3} y}{d x ^{3}} + 3 \frac{d ^{2} y}{d x ^{2}} - 4 y = 0

What is the solution for y^{'''}+5y^{''}-y^'-5y=0 ?
The solution for y^{'''}+5y^{''}-y^'-5y=0 is y=c_{1}e^{-5t}+c_{2}e^{-t}+c_{3}e^t