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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 8 y + 16 y = t^{- 3} e^{4 t}

x^{^{''}} + 240 x^{^{'}} - 9.8 = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{2} e^{3} t, y (0) = 2, y^{^{'}} (0) = 17

y^{^{''}} + 6 y^{^{'}} + 13 y = e^{- 3 x} (cos (2 x))

y^{^{''}} + 36 y = sec^{2} (x)

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