What is the solution for y^{''}+9y^'+8y=3e^{5x} ?

The solution for y^{''}+9y^'+8y=3e^{5x} is y=c_{1}e^{-x}+c_{2}e^{-8x}+1/26 e^{5x}

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y^{''}+9y^'+8y=3e^{5x}

y^{^{''}} + 9 y^{^{'}} + 8 y = 3 e^{5 x}

y = c_{1} e^{- x} + c_{2} e^{- 8 x} + \frac{1}{26} e^{5 x}

Solution steps

y^{''} (x) + 9 y^{'} (x) + 8 y = 3 e^{5 x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 8 x} + \frac{1}{26} e^{5 x}

y = c_{1} e^{- x} + c_{2} e^{- 8 x} + \frac{1}{26} e^{5 x}

y^{^{''}} - 6 y^{^{'}} + 25 y = 2 sin (t) - cos (t)

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

u^{''} - u^{'} + 4 H (t (x)) = e^{5 t (x)}

y^{^{''}} - 2 y^{^{'}} + 17 y = e^{x} sin (x)

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 + e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}+9y^'+8y=3e^{5x} ?
The solution for y^{''}+9y^'+8y=3e^{5x} is y=c_{1}e^{-x}+c_{2}e^{-8x}+1/26 e^{5x}