What is the solution for y^{''}+6y^'+9y=1+x ?

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

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y^{''}+6y^'+9y=1+x

y^{^{''}} + 6 y^{^{'}} + 9 y = 1 + x

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

Solution steps

y^{''} (x) + 6 y^{'} (x) + 9 y = 1 + x

Solve linear ODE:

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

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

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