What is the solution for 9y^{''}+6y^'+y=x^2 ?

The solution for 9y^{''}+6y^'+y=x^2 is y=c_{1}e^{-x/3}+c_{2}e^{-x/3}x+x^2-12x+54

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9y^{''}+6y^'+y=x^2

9 y^{^{''}} + 6 y^{^{'}} + y = x^{2}

y = c_{1} e^{- \frac{x}{3}} + c_{2} e^{- \frac{x}{3}} x + x^{2} - 12 x + 54

Solution steps

9 y^{''} (x) + 6 y^{'} (x) + y = x^{2}

Solve linear ODE:

y = c_{1} e^{- \frac{x}{3}} + c_{2} e^{- \frac{x}{3}} x + x^{2} - 12 x + 54

y = c_{1} e^{- \frac{x}{3}} + c_{2} e^{- \frac{x}{3}} x + x^{2} - 12 x + 54

What is the solution for 9y^{''}+6y^'+y=x^2 ?
The solution for 9y^{''}+6y^'+y=x^2 is y=c_{1}e^{-x/3}+c_{2}e^{-x/3}x+x^2-12x+54