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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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