What is the solution for y^{''}+2y^'+y=x^{-6}e^{-x} ?

The solution for y^{''}+2y^'+y=x^{-6}e^{-x} is y=c_{1}e^{-x}+c_{2}xe^{-x}+(e^{-x})/(20x^4)

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y^{''}+2y^'+y=x^{-6}e^{-x}

y^{^{''}} + 2 y^{^{'}} + y = x^{- 6} e^{- x}

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

Solution steps

y^{''} (x) + 2 y^{'} (x) + y = x^{- 6} e^{- x}

Solve linear ODE:

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

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

\int \frac{x + 2}{x ^{2} + 3 x - 4} d x

\frac{\partial}{\partial x} (\frac{4}{36 - x ^{2}})

(2) (- 3.1)

\int cos^{7} (8 - x) sin (8 - x) d x

y^{^{'}} - 4 y = 9 e^{7 t}

What is the solution for y^{''}+2y^'+y=x^{-6}e^{-x} ?
The solution for y^{''}+2y^'+y=x^{-6}e^{-x} is y=c_{1}e^{-x}+c_{2}xe^{-x}+(e^{-x})/(20x^4)