What is the solution for y^{''}+6y^'+8y=e^{-5x} ?

The solution for y^{''}+6y^'+8y=e^{-5x} is y=c_{1}e^{-2x}+c_{2}e^{-4x}+1/3 e^{-5x}

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y^{''}+6y^'+8y=e^{-5x}

y^{^{''}} + 6 y^{^{'}} + 8 y = e^{- 5 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x} + \frac{1}{3} e^{- 5 x}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 8 y = e^{- 5 x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x} + \frac{1}{3} e^{- 5 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x} + \frac{1}{3} e^{- 5 x}

\frac{d}{d x} (6 x^{70})

y^{^{''}} - y^{^{'}} - 2 y = - 2 t + 10 t^{2}

\int \frac{1}{5 x + 16} d x

y = 9 x^{2}, y = x^{2} + 7

h \to 0 lim (2 x h)

What is the solution for y^{''}+6y^'+8y=e^{-5x} ?
The solution for y^{''}+6y^'+8y=e^{-5x} is y=c_{1}e^{-2x}+c_{2}e^{-4x}+1/3 e^{-5x}