What is the solution for (D^2+4D+4)y=5e^{3x} ?

The solution for (D^2+4D+4)y=5e^{3x} is y=c_{1}e^{-2x}+c_{2}xe^{-2x}+1/5 e^{3x}

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(D^2+4D+4)y=5e^{3x}

(D^{2} + 4 D + 4) y = 5 e^{3 x}

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

Solution steps

(D^{2} + 4 D + 4) y = 5 e^{3 x}

Solve linear ODE:

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

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

3 y^{^{'}} + 2 y^{^{''}} = - 1000 cos (3.14 \cdot \frac{t}{0.2})

y^{^{''}} - \frac{1}{2} y^{^{'}} - 1 = 0, y (0) = 100, y (3) = 10

\frac{1}{2} y^{^{''}} + 2 y = 3 tan (2 t) - \frac{1}{2} e^{2 t}

y^{^{''}} + 4 y^{^{'}} + y = - 9

y^{^{'''}} + 4 y^{^{'}} = sin (x) \cdot cos (x)

What is the solution for (D^2+4D+4)y=5e^{3x} ?
The solution for (D^2+4D+4)y=5e^{3x} is y=c_{1}e^{-2x}+c_{2}xe^{-2x}+1/5 e^{3x}