What is the solution for D^2(D+4)^2y=0 ?

The solution for D^2(D+4)^2y=0 is y=c_{1}+c_{2}x+c_{3}e^{-4x}+c_{4}xe^{-4x}

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D^2(D+4)^2y=0

D^{2} (D + 4)^{2} y = 0

y = c_{1} + c_{2} x + c_{3} e^{- 4 x} + c_{4} x e^{- 4 x}

Solution steps

D^{2} (D + 4)^{2} y = 0

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} e^{- 4 x} + c_{4} x e^{- 4 x}

y = c_{1} + c_{2} x + c_{3} e^{- 4 x} + c_{4} x e^{- 4 x}

u^{^{''}} + 23 H (t) = 0

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = 0, y (0) = 2

x^{^{''}} + 3 x^{^{'}} - 4 x = 0

y^{^{''}} + 16 y^{^{'}} + 73 y = 0, y (0) = 4

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9

What is the solution for D^2(D+4)^2y=0 ?
The solution for D^2(D+4)^2y=0 is y=c_{1}+c_{2}x+c_{3}e^{-4x}+c_{4}xe^{-4x}