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}

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