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) \cdot 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}

y^{^{''}} - 7 y^{^{'}} + 15 y = 0

y^{^{''}} + 4 y^{^{'}} + 2.5 y = 0

(d^{3} + d^{2} + 4 d + 4) \cdot y = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{'}} (0) = - 1

(d^{3} - 5 d^{2} + 8 d - 4) \cdot y = 0

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}