What is the solution for y^{''}+6y^'+9y=x ?

The solution for y^{''}+6y^'+9y=x is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+x/9-2/27

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y^{''}+6y^'+9y=x

y^{^{''}} + 6 y^{^{'}} + 9 y = x

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{x}{9} - \frac{2}{27}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 9 y = x

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{x}{9} - \frac{2}{27}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{x}{9} - \frac{2}{27}

y^{^{''}} + 3 y = 11

x^{^{''}} + 2 x^{^{'}} + 2 x = 2, x (0) = 0, x^{^{'}} (0) = 0

(d^{2} - 4 d + 3) y = e^{2 t}

y^{^{''}} = 2 y + tan^{3} (x), y^{1} (x) = \frac{1}{2} tan (x)

y^{^{''}} - 2 y + y = \frac{e ^{x}}{1 + x ^{2}}

What is the solution for y^{''}+6y^'+9y=x ?
The solution for y^{''}+6y^'+9y=x is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+x/9-2/27