What is the solution for y^{''}+6y^'+8y=e^{2x} ?

The solution for y^{''}+6y^'+8y=e^{2x} is y=c_{1}e^{-2x}+c_{2}e^{-4x}+1/24 e^{2x}

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y^{''}+6y^'+8y=e^{2x}

y^{^{''}} + 6 y^{^{'}} + 8 y = e^{2 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x} + \frac{1}{24} e^{2 x}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 8 y = e^{2 x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x} + \frac{1}{24} e^{2 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x} + \frac{1}{24} e^{2 x}

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = - 1, y^{^{'}} (0) = 4

\int e^{2 - 5 x} d x

x \to 2 + lim (\frac{1}{x ^{2} - 5 x + 6})

2 y^{^{''}} + (a + 1) y = 0

\int {\frac{3 - x}{x ^{2} + 1} + x ln (x^{2})} d x

What is the solution for y^{''}+6y^'+8y=e^{2x} ?
The solution for y^{''}+6y^'+8y=e^{2x} is y=c_{1}e^{-2x}+c_{2}e^{-4x}+1/24 e^{2x}