What is the solution for y^{'''}-3y^{''}-9y^'+27y=0 ?

The solution for y^{'''}-3y^{''}-9y^'+27y=0 is y=c_{1}e^{-3t}+c_{2}e^{3t}+c_{3}te^{3t}

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y^{'''}-3y^{''}-9y^'+27y=0

y^{^{'''}} - 3 y^{^{''}} - 9 y^{^{'}} + 27 y = 0

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

Solution steps

y^{'''} (t) - 3 y^{''} (t) - 9 y^{'} (t) + 27 y = 0

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (2 x yz)

4 x + \frac{1}{x}

\int \frac{6 + 6 x}{1 + x ^{2}} d x

- \frac{13}{s ^{5}}

ln (1 + x)

What is the solution for y^{'''}-3y^{''}-9y^'+27y=0 ?
The solution for y^{'''}-3y^{''}-9y^'+27y=0 is y=c_{1}e^{-3t}+c_{2}e^{3t}+c_{3}te^{3t}