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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d}{d x} (arcsin (8 x))

e^{- \frac{5}{t ^{7}}}

ln (2 x - 1)

\int - x^{7} e^{x^{8} - 7} - 2 x d x

\frac{d}{d x} (\frac{cos ( x )}{2 sin ^{2} ( x )})

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