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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to 2 lim (\frac{3 ^{x} - 9}{x - 2})

\frac{\partial}{\partial x} (9 x e^{x^{2} + y^{2}})

\frac{d}{d x} (\frac{1}{5} x^{5} - 2 x^{3} + 3 x)

x \to - 1 lim (6 x + 3)

x \to 1 lim (\frac{e ^{x}}{1 - x})

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