What is the solution for (D^3-6D^2+11D-6)y=0 ?

The solution for (D^3-6D^2+11D-6)y=0 is y=c_{1}e^x+c_{2}e^{2x}+c_{3}e^{3x}

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(D^3-6D^2+11D-6)y=0

(D^{3} - 6 D^{2} + 11 D - 6) y = 0

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

Solution steps

(D^{3} - 6 D^{2} + 11 D - 6) y = 0

Solve linear ODE:

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

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

20 y^{^{''}} + 240 y^{^{'}} + 800 y = 0

a y^{^{''}} + b y^{^{'}} - cy = 0

y^{^{''}} - 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 3, y (0) = 5

y^{^{''}} + 1 y = 0, y (\frac{π}{2}) = 2, y^{^{'}} (\frac{π}{2}) = 3

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = \frac{5}{2}

What is the solution for (D^3-6D^2+11D-6)y=0 ?
The solution for (D^3-6D^2+11D-6)y=0 is y=c_{1}e^x+c_{2}e^{2x}+c_{3}e^{3x}