What is the solution for y^{''}-2y^'+y=t^{-6}e^t ?

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

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y^{''}-2y^'+y=t^{-6}e^t

y^{^{''}} - 2 y^{^{'}} + y = t^{- 6} e^{t}

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

Solution steps

y^{''} (t) - 2 y^{'} (t) + y = t^{- 6} e^{t}

Solve linear ODE:

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

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

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