What is the solution for (D^2+7D+6)y=e^{2x} ?

The solution for (D^2+7D+6)y=e^{2x} is y=c_{1}e^{-x}+c_{2}e^{-6x}+1/24 e^{2x}

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(D^2+7D+6)y=e^{2x}

(D^{2} + 7 D + 6) y = e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{- 6 x} + \frac{1}{24} e^{2 x}

Solution steps

(D^{2} + 7 D + 6) y = e^{2 x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 6 x} + \frac{1}{24} e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{- 6 x} + \frac{1}{24} e^{2 x}

y^{^{''}} - 2 y^{^{'}} + y = ln (x)

y^{^{''}} = 2 y + 18 tan^{3} (x)

y^{^{''}} + 2 y^{^{'}} - 2 y = e^{- 2 x} (3 x^{2} + 5 x + 2)

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (x) + e^{x}

5 y^{^{''}} + 25 y^{^{'}} + \frac{1}{1 0 ^{- 2}} y = 10 e^{- \frac{x}{4}}

What is the solution for (D^2+7D+6)y=e^{2x} ?
The solution for (D^2+7D+6)y=e^{2x} is y=c_{1}e^{-x}+c_{2}e^{-6x}+1/24 e^{2x}