What is the solution for y^{'''}-6y^{''}+11y^'-6y=0 ?

The solution for y^{'''}-6y^{''}+11y^'-6y=0 is y=c_{1}e^t+c_{2}e^{2t}+c_{3}e^{3t}

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y^{'''}-6y^{''}+11y^'-6y=0

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = 0

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

Solution steps

y^{'''} (t) - 6 y^{''} (t) + 11 y^{'} (t) - 6 y = 0

Solve linear ODE:

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

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

\int_{- 5}^{1} (2 x + 6) d x

\frac{7}{t}

\frac{1}{2} t^{2}

y = 2 x - 1, x = 2, x = 5, y = 0

\frac{d x}{d t} = e^{3 t + 2 x}

What is the solution for y^{'''}-6y^{''}+11y^'-6y=0 ?
The solution for y^{'''}-6y^{''}+11y^'-6y=0 is y=c_{1}e^t+c_{2}e^{2t}+c_{3}e^{3t}