What is the solution for y^{'''}+5y^{''}-34y^'-80y=0 ?

The solution for y^{'''}+5y^{''}-34y^'-80y=0 is y=c_{1}e^{-2t}+c_{2}e^{5t}+c_{3}e^{-8t}

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y^{'''}+5y^{''}-34y^'-80y=0

y^{^{'''}} + 5 y^{^{''}} - 34 y^{^{'}} - 80 y = 0

y = c_{1} e^{- 2 t} + c_{2} e^{5 t} + c_{3} e^{- 8 t}

Solution steps

y^{'''} (t) + 5 y^{''} (t) - 34 y^{'} (t) - 80 y = 0

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{5 t} + c_{3} e^{- 8 t}

y = c_{1} e^{- 2 t} + c_{2} e^{5 t} + c_{3} e^{- 8 t}

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

- 2 y^{^{''}} - 10 y^{^{'}} + \frac{5}{2} y = 0

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

x^{^{'''}} + x^{^{''}} - 6 x^{^{'}} = 0

4 y^{^{''}} - y^{^{'}} + 17 y = 0

What is the solution for y^{'''}+5y^{''}-34y^'-80y=0 ?
The solution for y^{'''}+5y^{''}-34y^'-80y=0 is y=c_{1}e^{-2t}+c_{2}e^{5t}+c_{3}e^{-8t}