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

The solution for y^{''}+8y^'-9y=e^{3x} is y=c_{1}e^x+c_{2}e^{-9x}+1/24 e^{3x}

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

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

y = c_{1} e^{x} + c_{2} e^{- 9 x} + \frac{1}{24} e^{3 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 9 x} + \frac{1}{24} e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- 9 x} + \frac{1}{24} e^{3 x}

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What is the solution for y^{''}+8y^'-9y=e^{3x} ?
The solution for y^{''}+8y^'-9y=e^{3x} is y=c_{1}e^x+c_{2}e^{-9x}+1/24 e^{3x}