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

The solution for y^{''}+6y^'+9y=5+5x is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+(5x)/9+5/27

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

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

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{5 x}{9} + \frac{5}{27}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{5 x}{9} + \frac{5}{27}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{5 x}{9} + \frac{5}{27}

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 15 t

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

y^{^{''''}} + 8 y^{^{''}} + 16 y = 48 + cos (4 t)

y^{^{''}} + 16 y = 32 t

y^{^{''}} + 4 y^{^{'}} + 6 y = 4 e^{- 2 x} cos (x)

What is the solution for y^{''}+6y^'+9y=5+5x ?
The solution for y^{''}+6y^'+9y=5+5x is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+(5x)/9+5/27