What is the solution for y^{''}+9y^'+18y=x+e^{-x} ?

The solution for y^{''}+9y^'+18y=x+e^{-x} is y=c_{1}e^{-3x}+c_{2}e^{-6x}+x/(18)-1/36+1/10 e^{-x}

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y^{''}+9y^'+18y=x+e^{-x}

y^{^{''}} + 9 y^{^{'}} + 18 y = x + e^{- x}

y = c_{1} e^{- 3 x} + c_{2} e^{- 6 x} + \frac{x}{18} - \frac{1}{36} + \frac{1}{10} e^{- x}

Solution steps

y^{''} (x) + 9 y^{'} (x) + 18 y = x + e^{- x}

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} e^{- 6 x} + \frac{x}{18} - \frac{1}{36} + \frac{1}{10} e^{- x}

y = c_{1} e^{- 3 x} + c_{2} e^{- 6 x} + \frac{x}{18} - \frac{1}{36} + \frac{1}{10} e^{- x}

y^{^{''}} + 49 y = 4 t^{3} sin (7 t)

(D^{2} + 1) y = sec (x tan (x))

4 x^{^{''}} + k x = 8 sin (t)

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

y^{^{''}} + 4 y = \frac{5}{2} cos (2 t)

What is the solution for y^{''}+9y^'+18y=x+e^{-x} ?
The solution for y^{''}+9y^'+18y=x+e^{-x} is y=c_{1}e^{-3x}+c_{2}e^{-6x}+x/(18)-1/36+1/10 e^{-x}