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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} - 15 y = 384 e^{- t}

y^{^{''}} + 4 y = - 1, y (\frac{π}{8}) = \frac{3}{4}, y^{^{'}} (\frac{π}{8}) = 2

y^{^{''}} + 5 y^{^{'}} + 4 y = 12

y^{^{''}} - 22 y^{^{'}} + 121 y = \frac{e ^{- 11 x}}{1 + x ^{2}}

x^{^{''}} - x = sin (t)

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