What is the solution for y^{''}-6y^'+9y=t^{-6}e^{3t} ?

The solution for y^{''}-6y^'+9y=t^{-6}e^{3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+(e^{3t})/(20t^4)

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y^{''}-6y^'+9y=t^{-6}e^{3t}

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 6} e^{3 t}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3 t}}{20 t ^{4}}

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = t^{- 6} e^{3 t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3 t}}{20 t ^{4}}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3 t}}{20 t ^{4}}

y^{^{''}} + 5 y^{^{'}} + 6 y = 12 e^{t}, y (0) = - 11, y (0) = 31

y^{^{''}} + y^{^{'}} - y = t^{3}

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{x s e c (x)}

y^{^{''}} + y^{^{'}} = e^{2 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 3 t^{2} + 4 + e^{2 t} + t sin (2 t)

What is the solution for y^{''}-6y^'+9y=t^{-6}e^{3t} ?
The solution for y^{''}-6y^'+9y=t^{-6}e^{3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+(e^{3t})/(20t^4)