What is the solution for 9y^{''}-6y^'+y=5-x ?

The solution for 9y^{''}-6y^'+y=5-x is y=c_{1}e^{x/3}+c_{2}e^{x/3}x-x-1

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9y^{''}-6y^'+y=5-x

9 y^{^{''}} - 6 y^{^{'}} + y = 5 - x

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

Solution steps

9 y^{''} (x) - 6 y^{'} (x) + y = 5 - x

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} + 2 y = sin (x), y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + 2 y^{^{'}} + 2 y = 3 e^{- x}

y^{^{''}} - 6 y^{^{'}} + 8 y = 3 sin (2 x)

y^{^{''}} + 2 y^{^{'}} + y = 2 e^{- x} - e^{x}

y^{^{''}} + 2 y = - 4 x + 10

What is the solution for 9y^{''}-6y^'+y=5-x ?
The solution for 9y^{''}-6y^'+y=5-x is y=c_{1}e^{x/3}+c_{2}e^{x/3}x-x-1