What is the solution for (D^3-5D^2+8D-4)y=0 ?

The solution for (D^3-5D^2+8D-4)y=0 is y=c_{1}e^x+c_{2}e^{2x}+c_{3}xe^{2x}

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(D^3-5D^2+8D-4)y=0

(D^{3} - 5 D^{2} + 8 D - 4) y = 0

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

Solution steps

(D^{3} - 5 D^{2} + 8 D - 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^{^{''}} + b \cdot y = 0, y (0) - 9 y^{^{'}} (0) = 0, y^{^{'}} (9) = 0

y^{^{'''}} + 6 y^{^{''}} + 9 y^{^{'}} + 4 y = 0

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = 6, y^{^{'}} (0) = 2

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} = 0

y^{^{''}} + 0.8 y^{^{'}} + 100 y = 0, y (0) = 0, y^{^{'}} (0) = 4

What is the solution for (D^3-5D^2+8D-4)y=0 ?
The solution for (D^3-5D^2+8D-4)y=0 is y=c_{1}e^x+c_{2}e^{2x}+c_{3}xe^{2x}