What is the solution for y^{''}-9y=5e^{3x} ?

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

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y^{''}-9y=5e^{3x}

y^{^{''}} - 9 y = 5 e^{3 x}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{5 e ^{3 x} x}{6}

Solution steps

y^{''} (x) - 9 y = 5 e^{3 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{5 e ^{3 x} x}{6}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{5 e ^{3 x} x}{6}

y^{^{'''}} + 9 y^{^{''}} + 27 y^{^{'}} + 27 y = 3 e^{- 3 x}

y^{^{''}} + 16 y = 6 sin (4 x)

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

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = x e^{x} - e^{x} + 7

(D^{2} - D - 2) y = 36 x e^{2 x}

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