What is the solution for y^{''}-6y^'+9y=t^{-7}e^{3t} ?

The solution for y^{''}-6y^'+9y=t^{-7}e^{3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+(e^{3t})/(30t^5)

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y^{''}-6y^'+9y=t^{-7}e^{3t}

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 7} e^{3 t}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3 t}}{30 t ^{5}}

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = t^{- 7} e^{3 t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3 t}}{30 t ^{5}}

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + \frac{e ^{3 t}}{30 t ^{5}}

x^{^{''}} + 2 x^{^{'}} - 4 x = 6 e^{3 t} - 4 t + 3

y^{^{''}} + 4 y^{^{'}} + 5 y = 3 t + e^{t}

y^{^{''}} - 25 y = 3 x^{2} - 2 + e^{x}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 4 y = 8 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 40 y = 25 sin (6 t)

What is the solution for y^{''}-6y^'+9y=t^{-7}e^{3t} ?
The solution for y^{''}-6y^'+9y=t^{-7}e^{3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+(e^{3t})/(30t^5)