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}

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

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

\int \frac{x ^{2} + 4}{x + 1} d x

d er i v a t i v e g (x) = x^{2} (1 - 7 x)

\frac{d}{d x} ((\frac{x + 7}{x - 7})^{5})

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}