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}

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = - 1, y^{^{'}} (0) = 17

y^{^{'''}} - 3 y^{^{''}} - 25 y^{^{'}} - 21 y = 0

0.5 y^{^{''}} + 6 y^{^{'}} + 50 y = 0

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

\frac{d ^{3} y}{d x ^{3}} = \frac{d y}{d x}

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