What is the solution for (D^2-9D+18)y=e^{e^{-3x}} ?

The solution for (D^2-9D+18)y=e^{e^{-3x}} is y=c_{1}e^{6x}+c_{2}e^{3x}+(e^{6x+e^{-3x}})/9

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(D^2-9D+18)y=e^{e^{-3x}}

(D^{2} - 9 D + 18) y = e^{e^{- 3 x}}

y = c_{1} e^{6 x} + c_{2} e^{3 x} + \frac{e ^{6 x + e^{- 3 x}}}{9}

Solution steps

(D^{2} - 9 D + 18) y = e^{e^{- 3 x}}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{3 x} + \frac{e ^{6 x + e^{- 3 x}}}{9}

y = c_{1} e^{6 x} + c_{2} e^{3 x} + \frac{e ^{6 x + e^{- 3 x}}}{9}

What is the solution for (D^2-9D+18)y=e^{e^{-3x}} ?
The solution for (D^2-9D+18)y=e^{e^{-3x}} is y=c_{1}e^{6x}+c_{2}e^{3x}+(e^{6x+e^{-3x}})/9