What is the solution for y^{''}-16y=e^{-5x}(-8-9x) ?

The solution for y^{''}-16y=e^{-5x}(-8-9x) is y=c_{1}e^{4x}+c_{2}e^{-4x}-e^{-5x}x-2e^{-5x}

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y^{''}-16y=e^{-5x}(-8-9x)

y^{^{''}} - 16 y = e^{- 5 x} (- 8 - 9 x)

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - e^{- 5 x} x - 2 e^{- 5 x}

Solution steps

y^{''} (x) - 16 y = e^{- 5 x} (- 8 - 9 x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - e^{- 5 x} x - 2 e^{- 5 x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - e^{- 5 x} x - 2 e^{- 5 x}

y^{^{'''}} - 3 y^{^{''}} + 2 y = e^{- 4 t}

y^{^{''}} + 2 y = cos (2) t + sin (2) t

y^{^{''}} + 25 y = 7 sec (5 x)

2 y^{^{''}} + 3 y^{^{'}} + y = x^{2}, y (0) = 0, y^{^{'}} (0) = 1

(d^{2} - 1) y = sin^{2} (x)

What is the solution for y^{''}-16y=e^{-5x}(-8-9x) ?
The solution for y^{''}-16y=e^{-5x}(-8-9x) is y=c_{1}e^{4x}+c_{2}e^{-4x}-e^{-5x}x-2e^{-5x}