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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 24 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = 22

\frac{d ^{2} y}{d x ^{2}} - a y = 0

6 \frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - y = 0

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} + 6 y = 0

(D^{2} + 1) y = 0

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