What is the solution for y^{''}+9y^'+14y=e^{-x} ?

The solution for y^{''}+9y^'+14y=e^{-x} is y=c_{1}e^{-2x}+c_{2}e^{-7x}+1/6 e^{-x}

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y^{''}+9y^'+14y=e^{-x}

y^{^{''}} + 9 y^{^{'}} + 14 y = e^{- x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 7 x} + \frac{1}{6} e^{- x}

Solution steps

y^{''} (x) + 9 y^{'} (x) + 14 y = e^{- x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 7 x} + \frac{1}{6} e^{- x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 7 x} + \frac{1}{6} e^{- x}

y^{^{''}} - y^{^{'}} = - 3 x^{2}

d, d (t) = 5 t^{2} + 10 - 12

\frac{d ^{2} y}{d x ^{2}} - 9 y = 54

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{e^{x}}

\frac{1}{6} y^{^{''}} + 6 y = 3 tan (6 t) - \frac{1}{3} e^{4 t}

What is the solution for y^{''}+9y^'+14y=e^{-x} ?
The solution for y^{''}+9y^'+14y=e^{-x} is y=c_{1}e^{-2x}+c_{2}e^{-7x}+1/6 e^{-x}