What is the solution for (D^2+5D+6)y=e^{2x} ?

The solution for (D^2+5D+6)y=e^{2x} is y=c_{1}e^{-2x}+c_{2}e^{-3x}+1/20 e^{2x}

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(D^2+5D+6)y=e^{2x}

(D^{2} + 5 D + 6) y = e^{2 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{20} e^{2 x}

Solution steps

(D^{2} + 5 D + 6) y = e^{2 x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{20} e^{2 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{20} e^{2 x}

25 y^{^{''}} - y = \frac{x e x}{5}

y^{^{''}} - 2 y^{^{'}} + y = e^{x} + e^{2 x}

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{x} (0 = (2 x))

y^{^{''}} - 6 y^{^{'}} + 9 y = 18

y^{^{''}} - y = 8 t e^{t} + 2 e^{t}

What is the solution for (D^2+5D+6)y=e^{2x} ?
The solution for (D^2+5D+6)y=e^{2x} is y=c_{1}e^{-2x}+c_{2}e^{-3x}+1/20 e^{2x}