What is the solution for y^{''}-2y^'-8y=4e^2-21e^{-3x} ?

The solution for y^{''}-2y^'-8y=4e^2-21e^{-3x} is y=c_{1}e^{4x}+c_{2}e^{-2x}-(e^2)/2-3e^{-3x}

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y^{''}-2y^'-8y=4e^2-21e^{-3x}

y^{^{''}} - 2 y^{^{'}} - 8 y = 4 e^{2} - 21 e^{- 3 x}

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - \frac{e ^{2}}{2} - 3 e^{- 3 x}

Solution steps

y^{''} (x) - 2 y^{'} (x) - 8 y = 4 e^{2} - 21 e^{- 3 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - \frac{e ^{2}}{2} - 3 e^{- 3 x}

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - \frac{e ^{2}}{2} - 3 e^{- 3 x}

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

(y^{^{''}}) + y = 3 x sin (x)

y^{^{''}} + 500 y^{^{'}} + 20000 y = 1100

y^{^{''}} + 2 y^{^{'}} - 8 y = x + 1

y^{^{''}} - y^{^{'}} - 6 y = 15 sin (3 x)

What is the solution for y^{''}-2y^'-8y=4e^2-21e^{-3x} ?
The solution for y^{''}-2y^'-8y=4e^2-21e^{-3x} is y=c_{1}e^{4x}+c_{2}e^{-2x}-(e^2)/2-3e^{-3x}