What is the solution for (D^4+D^3-3D^2-5D-2)y=0 ?

The solution for (D^4+D^3-3D^2-5D-2)y=0 is y=c_{1}e^{2x}+c_{2}e^{-x}+c_{3}xe^{-x}+c_{4}x^2e^{-x}

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(D^4+D^3-3D^2-5D-2)y=0

(D^{4} + D^{3} - 3 D^{2} - 5 D - 2) y = 0

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

Solution steps

(D^{4} + D^{3} - 3 D^{2} - 5 D - 2) y = 0

Solve linear ODE:

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

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

x^{^{''}} + 5 x^{^{'}} + 6 x = 0, x (0) = 2, x^{^{'}} (0) = 3

625 y^{^{''''}} - y = 0

10 y^{^{''}} + 9 y^{^{'}} + 2 y^{^{'}} = 0

0.1 y^{^{''}} + y^{^{'}} + y = 0

4 y^{^{''}} + 14 y^{^{'}} - 8 y = 0

What is the solution for (D^4+D^3-3D^2-5D-2)y=0 ?
The solution for (D^4+D^3-3D^2-5D-2)y=0 is y=c_{1}e^{2x}+c_{2}e^{-x}+c_{3}xe^{-x}+c_{4}x^2e^{-x}